<?xml version="1.0" encoding="UTF-8"?> 
<fps version="1.1" url="http://code.google.com/p/freeproblemset/">
	<generator name="HUSTOJ" url="http://code.google.com/p/hustoj/"/>
	<item>
<title><![CDATA[Equations]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[128]]></memory_limit>

<description><![CDATA[<p>Given 2 equations on the variables</p>
<i>x</i>
<p>and</p>
<i>y</i>
<p>, solve for</p>
<i>x</i>
<p>and</p>
<i>y</i>
<p>.</p>
<p>The first line of input contains N, the number of test cases.  Each test case consists of two equations, each on a separate line.  An empty line separates cases.  An equation consists of two or more terms separated by addition,  subtraction, or equality operators.  A term is an integer, or a variable name (<i>x</i> or <i>y</i>) optionally preceded by a minus sign or an integer coefficient.  There is exactly one equality operator.  All operators are surrounded by spaces, and there are no spaces within terms.  For each case, print two lines, giving the values of <i>x</i> and <i>y</i> as rationals in simplest terms.  If <i>x</i> or <i>y</i> has no unique rational value such that both equations hold, print &quot;don't know&quot; for its value.  Print an empty line between cases.</p>]]></description>
<input><![CDATA[]]></input> 
<output><![CDATA[]]></output>
<sample_input><![CDATA[7
2x + 3y = x
5 = x + y + 3

2x + 3y = 0
10x = -15y

2x + 3y = 0
10x = -15y + 1

x = 1
3x = 6y

2x = 3x + -x + y
x + y = x + y

2x = -3
-2y = 3

1 = 2
x = 3
]]></sample_input>
<sample_output><![CDATA[3
-1

don't know
don't know

don't know
don't know

1
1/2

don't know
0

-3/2
-3/2

don't know
don't know
]]></sample_output>
<test_input><![CDATA[65
2x + 3y = 2x + 3y + 1
x = 2

2x + 3y = x
5 = x + y + 3

2x + 3y = 0
10x = -15y

2x + 3y = 0
10x = -15y + 1

x = 1
3x = 6y

2x = 3x - x + y
x + y = x + y

x = 3
x = y

x = 3
x = x

x = x
x = 3

y = 6
y = y

y = y
y = 6

y = 6
y = 6

x = y
y = x

x = 3
x = 4

x = 3
y = 6

77x + 35x - -51x - -73y = -41y - 40
-89y + -71y - -38x = -33x + -98

67x - -89x + 73 + 84x = 98y + 70y - -9y - -27y - 96x
-16 = 36y

13y - -5 = 45y + -66y + 50x - -24y - 84
99 - -24 = 39x - 86 + 95x - 78y + -3y

-48y + -20y + -35y = -56y - 29 + -3y
9x + -44y = 53

-17y = -76x + 32y
-30 - 15x + 96y - -55y = -49x + 79x - -72x - 93x - 64

-44 + -73x + 36x + -63x + -93 = 21y + -71x + 93y
-89 + 76x + 63y - -94x = 4x - -12 + 17 - 43

-x + -56 + 39y - -31y = 42y
55x - -89y - -1 = 46y - -78y - -95x

-22y - 36x = -74
-84 = -42y + -38y - -64y + 79x

73y + 30x - -40 + 81y = 96 + -87
26y = -16

76 = 36x + 56x - -13y - 72 + 36y
-94 + 72x + -81x = 21y + -89y + 5

84x - -76x + 96x = -70y
-28y + 85y + -60y = -2y - 90 - -91

32x - -96y + -27y - -45x - 79x = 93x + 67y
54 + 44x - 6y + -58 = 28x - 8

-92x - 3x + -52 - 67 = 68 - -54
90x + 63y + -8 = 25y - 75y + 29x - -86 - 4y

48x - 94 + -57y = -98
-19y - 59y + 34x - -85 = 4y

-15x + 35 - -62y + -11y - -8y = 43 + 90 - 41 - -68y - 60
-19 - -75y + -23 - -74x = -43y - -95y

0 - 94x - 78x = 46x + 70
93x = -73y - -86x

-88 - 69 - 55y = -80
38x - -16y + -94x = -51y + -41y - 45 + -42y

-17x - 57x + 29 = -41y - -75 - -67x + -7 - -x
63x - 73x + -38 - -8x + 15y = 57x + 47x + -79y - -46y - 25x

-98 + 96x = 38x - -79
79 + 36 - -17y = 59 - -1 + 50y

5 = -51y + -95y + 75y - 89x
-95x - 82y - -7y - 93 = -47y - -86 + 77 + -12

-6y = 46y + -9x + 73y
10 = -83 + -45x

4y + -67 + -27 + -95x = -32y
95y = 49y + -74x

81x - -64y - 18 = 42y - 79
72y = -66x + -28x - -37y - -70x - -41

-18 - -96x + -2 = -60x + -38 + -59x + 24x - 54
65 + 76 = -82y + -47y + 59

20 - 34x = 91 - 15 + 89y
-84x + 39 = 78y

14 + -74x + -77x + 32y = -19 - 79y
31 + -6y + -97y + 82y + -85x = -75x

51 - 34 - -85x = 8 + 62x + 76x
87 - -79 + -40 = -89x - -15x - 83 - 16x - 25

-10y - -82y + 28 + 10x - -75y = 70
22 - -43 + 26y + -49 = 10 + 98 - 93 - 76x

-13 + -43x - -83y = 35 - 84
-34x - 28y = 93x

-28 + -100y + -17x = 27
34x - -79y = 85 - 61y - 41x - -50y

-83 + -85 + 64y = -37x - -63y + -72 - 87y - 41
11y + 61y + 12y = 6

-11x - 4 + 41y = 38y - 70y - 60y - -35 - -14y
35 + 93 + 9x + -36 - -5y = 13y - 49y + 93x - 60 + -14

40 + 61y + -50y - -25x = -58y + 19y - -31y
83y + 43 = 56x + -34y

92y - -32x - 74y = 18 + 77x - 73y
33 - -82 + 26y = 80

5y = -71y - 60y - 19 + 2x
83x = 40y + 38x

10y + -10y + -62x + -33 = -29 + -5x
54 + -68y - 73 + -37x + -6y = -y + -36 - -14x + 15

-66 + 22 = 73y + 42x
39 + -82y - -31y - 33 - -81y = -65x + -31y + -98x - -11 + 60y

-71x - -8y = 22x + 79 - 78
-18x = -1

53y - 94y - 7y + -36x - -20 = 94 + -63y
12y + 9y - -92x + 95y + -5x = 59y - -48y - 25y

-11 - -22 - 96y = 33x - -x
15y - -61y + 98y + -98y + 28y = -96y - -17x + -5y + 72x

25x - -55 - 39y + -97x + 42x = 39x - 96 + -6y + 19y
-68y = -21y + -65 - 7

76 - -99 - -8y = -4x
35y + -94x + -49y + 30x - 65y = 2y + 91y + -16x + 19x

-73 + 43x + 68 + -57x = 88 - -20x - -82x + -2y
79x = -34x

78x = 66 - 47y - -14
0 + 32y + 51x - -51x + 6 = -97 - -72 + -67x

-86y = -3y + -92y
-21 - 14y + 65y - -74 - -71x = 52y - 15 + -72 + -87y

86 = 63x - 97y + 82x
-74 = 65y

46x + -38x - -58 - -93 - -31x = -85y - 24 + -49 + 43 + -39x
-12y - 41x = 24

62y = -30x + -34 - 15y - 32x
-67x = -20x + -87 - -56y + 38

-89 - -19y = -17y + 35 - 69y + -28x
-77x = -43x + -61

71y = -82 - -17y + -3y + -26 + -10
29x - -8y + 49x = -78y - -57y + 66 - -47x - -80x
]]></test_input>
<test_output><![CDATA[don't know
don't know

3
-1

don't know
don't know

don't know
don't know

1
1/2

don't know
0

3
3

3
don't know

3
don't know

don't know
6

don't know
6

don't know
6

don't know
don't know

don't know
don't know

3
6

-8786/17087
6567/17087

-491/1008
-4/9

5119/2710
738/1355

82/9
29/44

-833/5150
-646/2575

5727/5699
-24917/17097

-92/55
747/385

-332/1157
4435/1157

829/390
-8/13

5213/6697
10440/6697

35/128
-1

4/269
190/269

-241/95
7877/3705

4517/1998
1972/999

103/107
-136/107

-35/109
245/7957

-165/56
-7/5

-314/3495
2237/3495

177/58
5/3

-17184/4253
21241/4253

-31/15
-93/625

-2162/3517
3478/3517

-3037/2307
1595/769

-72/191
-82/129

13/8
-5/4

1378/1427
4351/4281

don't know
don't know

-1239/10912
1601/5456

112/1305
-508/1305

1345/597
-557/597

341/259
1/14

21353/9545
5102/9545

-3863/3989
-3315/3989

-281/90
-35/26

-19/151
-171/1208

-4/57
106/1387

409/11857
-7382/11857

1/18
37/48

-2516/2529
2146/843

2255/15514
979/15514

3353/3243
72/47

-7525/38
11725/152

0
93/2

-309/419
1226/419

-140/71
0

-1588/9425
-74/65

132/2549
-5549/2549

811/21
-4636/147

61/34
418/595

-7184/2793
-118/57
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[http://plg1.cs.uwaterloo.ca/~acm00/020928/A.html]]></source>
<solution language="C"><![CDATA[#include <stdio.h>
#include <ctype.h>

int i,j,k,m,n,N;
char buf[10000];
char *b;
int val,sign,cx[2],cy[2],c[2],eq,state,coef,op;
int xnum,ynum,den;

int gcd(int a, int b){
   if (b == 0) return a;
   if (b < 0) return -gcd(a,-b);
   if (a < 0) return gcd(-a,b);
   return gcd(b,a%b);
}

void pr(int n, int d){
   if (n%d == 0) printf("%d\n",n/d);
   else printf("%d/%d\n",n/gcd(n,d),d/gcd(n,d));
}

main(){
   scanf("%d",&N); 
   gets(buf);
   while (N--) {
      if (m++) printf("\n");
      for (i=0;i<2;i++){
         gets(buf);
         b = buf;
         op = 1;
         eq = 1;
         cx[i] = cy[i] = c[i] = 0;
         while (*b) {
            while (*b == ' ') b++;
            sign = 1;
            if (*b == '+') {
               sign = 1;
               b++;
            } else if (*b == '-') {
               sign = -1;
               b++;
            }
            if (!isdigit(*b)) val = 1;
            else val = 0;
            while (isdigit(*b)) {
               val = val * 10 + (*b-'0');
               b++;
            }
            if (*b == 'x') {
               cx[i] += sign * op * val;
               b++;
            } else if (*b == 'y') {
               cy[i] += sign * op * val;
               b++;
            } else c[i] += sign * op * val;
            while (*b == ' ') b++;
            if (*b == '=') {
               eq = -1;
               op = -1;
               b++;
            } else if (*b == '+') {
               op = eq;
               b++;
            } else if (*b == '-') {
               op = -eq;
               b++;
            } else if (!*b) break;
            else printf("oops! at %s\n",b);
         }
         //printf("%dx + %dy + %d = 0\n",cx[i],cy[i],c[i]);
      }
      den = (cx[0]*cy[1]) - (cx[1] * cy[0]);
      if (den) {
         xnum = (-c[0]*cy[1]) - (-c[1] * cy[0]);
         ynum = (cx[0]*-c[1]) - (cx[1] * -c[0]);
         pr(xnum,den);
         pr(ynum,den);
      } else if (c[0] && !cx[0] && !cy[0] || cy[1] && !cx[1] && !cy[1]) {
         printf("don't know\ndon't know\n");
      } else {
         if (cx[0] && !cy[0] && !cx[1]) pr(-c[0],cx[0]);
         else if (cx[1] && !cy[1] && !cx[0]) pr(-c[1],cx[1]);
         else if (cx[1] && !cy[1] && cx[0] && !cy[0] && cx[1]*c[0] == cx[0]*c[1]) pr(-c[0],cx[0]);
         else printf("don't know\n");
         if (cy[0] && !cx[0] && !cy[1]) pr(-c[0],cy[0]);
         else if (cy[1] && !cx[1] && !cy[0]) pr(-c[1],cy[1]);
         else if (cy[1] && !cx[1] && cy[0] && !cx[0] && cy[1]*c[0] == cy[0]*c[1]) pr(-c[0],cy[0]);
         else printf("don't know\n");
      }
      gets(buf);
   }
}
]]></solution>
</item>
<item>
<title><![CDATA[Euclid's Game]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[128]]></memory_limit>

<description><![CDATA[<p>Two players, Stan and Ollie, play, starting with two natural numbers. Stan, the first player, subtracts any positive multiple of the lesser of the two numbers from the greater of the two numbers, provided that the resulting number must be nonnegative. Then Ollie, the second player, does the same with the two resulting numbers, then Stan, etc., alternately, until one player is able to subtract a multiple of the lesser number from the greater to reach 0, and thereby wins. For example, the players may start with (25,7):</p>
<pre>
         25 7
         11 7
          4 7
          4 3
          1 3
          1 0
</pre>
<p>an Stan wins.</p>
<p>The input consists of a number of lines.  Each line contains two positive integers giving the starting two numbers of the game. Stan always starts.</p>
<p>For each line of input, output one line saying either <tt>Stan wins</tt> or <tt>Ollie wins</tt> assuming that both of them play perfectly. The last line of input contains two zeroes and should not be processed.</p>]]></description>
<input><![CDATA[]]></input> 
<output><![CDATA[]]></output>
<sample_input><![CDATA[34 12
15 24
0 0
]]></sample_input>
<sample_output><![CDATA[Stan wins
Ollie wins
]]></sample_output>
<test_input><![CDATA[1111111111 2
1 1
36 20
28 20
25 7
4 4
8 4
12 8
20 8
34 12
15 24
846930886 1804289383
1714636915 1681692777
424238335 1957747793
1649760492 719885386
1189641421 596516649
1350490027 1025202362
1102520059 783368690
1967513926 2044897763
1540383426 1365180540
1303455736 304089172
521595368 35005211
1726956429 294702567
861021530 336465782
233665123 278722862
468703135 2145174067
1801979802 1101513929
635723058 1315634022
1125898167 1369133069
2089018456 1059961393
1656478042 628175011
1653377373 1131176229
1914544919 859484421
756898537 608413784
1973594324 1734575198
2038664370 149798315
184803526 1129566413
1424268980 412776091
749241873 1911759956
42999170 137806862
135497281 982906996
2084420925 511702305
1827336327 1937477084
1159126505 572660336
1632621729 805750846
1433925857 1100661313
84353895 1141616124
2001100545 939819582
1548233367 1998898814
1585990364 610515434
760313750 1374344043
356426808 1477171087
1889947178 945117276
709393584 1780695788
1918502651 491705403
1474612399 752392754
1264095060 2053999932
1843993368 1411549676
1984210012 943947739
1749698586 855636226
1956297539 1469348094
463480570 1036140795
1975960378 2040651434
1892066601 317097467
927612902 1376710097
603570492 1330573317
660260756 1687926652
485560280 959997301
593209441 402724286
894429689 1194953865
1947346619 364228444
270744729 221558440
1633108117 1063958031
2007905771 2114738097
822890675 1469834481
791698927 1610120709
498777856 631704567
524872353 1255179497
1572276965 327254586
1703964683 269455306
1600028624 352406219
2040332871 160051528
1120048829 112805732
515530019 378409503
1573363368 1713258270
2077486715 1409959708
1631518149 1373226340
289700723 200747796
168002245 1117142618
439493451 150122846
1760243555 990892921
1622597488 1231192379
338888228 111537764
438792350 2147469841
269441500 1911165193
116087764 2142757034
155324914 1869470124
1982275856 8936987
387346491 1275373743
841148365 350322227
1760281936 1960709859
1186452551 771151432
971899228 1244316437
213975407 1476153275
1626276121 1139901474
2130794395 653468858
1884661237 1239036029
1350573793 1605908235
1605894428 76065818
1987231011 1789366143
1784639529 1875335928
0 0
]]></test_input>
<test_output><![CDATA[Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Ollie wins
Ollie wins
Ollie wins
Ollie wins
Stan wins
Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins
Stan wins
Ollie wins
Ollie wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Ollie wins
Stan wins
Ollie wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Ollie wins
Ollie wins
Stan wins
Ollie wins
Ollie wins
Ollie wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Ollie wins
Ollie wins
Ollie wins
Ollie wins
Ollie wins
Stan wins
Stan wins
Stan wins
Ollie wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Stan wins
Ollie wins
Ollie wins
Ollie wins
Stan wins
Ollie wins
Stan wins
Ollie wins
Ollie wins
Stan wins
Ollie wins
Ollie wins
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C++"><![CDATA[#include <stdio.h>

int i,j,k,a,b;

int gcd(int a, int b) {
   if (b > a) return gcd(b,a);
   if (b == 0) return 0;  // this player loses
   if (a/b == 1) return !gcd(b,a%b); // no choice
   return 1; // this player can force a win
}

main(){
   while (2 == scanf("%d%d",&a,&b) && a) {
      if (gcd(a,b)%2) printf("Stan wins\n");
      else printf("Ollie wins\n");
   }
}
]]></solution>
</item>
<item>
<title><![CDATA[Arctic Network]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[128]]></memory_limit>

<description><![CDATA[<p>The Department of National Defence (DND) wishes to connect several northern outposts by a wireless network.  Two different communication technologies are to be used in establishing the network:  every outpost will have a  radio transceiver and some outposts will in addition have a satellite  channel.</p>
<p>Any two outposts with a satellite channel can communicate via the satellite, regardless of their location.  Otherwise, two  outposts can communicate by radio only if the distance between them does not exceed D, which depends of the power of the transceivers.   Higher power yields higher D but costs more.   Due to purchasing and maintenance considerations, the transceivers at the outposts must be identical; that is, the value of D is the same for every pair of outposts.</p>
<p>Your job is to determine the minimum D required for the transceivers.  There must be at least one communication path (direct or indirect) between every pair of outposts.</p>
<p>The first line of input contains N, the number of test cases.  The first line of each test case contains 1 &lt;= S &lt;= 100, the number of satellite channels,  and S &lt; P &lt;= 500, the number of outposts.  P lines follow, giving the (x,y) coordinates of each outpost in km (coordinates are integers between 0 and 10,000).   For each case, output should consist of a single line giving the minimum D required to connect the network. Output should be specified to 2 decimal points.</p>]]></description>
<input><![CDATA[]]></input> 
<output><![CDATA[]]></output>
<sample_input><![CDATA[1
2 4
0 100
0 300
0 600
150 750
]]></sample_input>
<sample_output><![CDATA[212.13
]]></sample_output>
<test_input><![CDATA[5
1 2
0 0
100 100
2 4
0 100
0 300
0 600
150 750
1 500
9383 886
2777 6915
7793 8335
5386 492
6649 1421
2362 27
8690 59
7763 3926
540 3426
9172 5736
5211 5368
2567 6429
5782 1530
2862 5123
4067 3135
3929 9802
4022 3058
3069 8167
1393 8456
5011 8042
6229 7373
4421 4919
3784 8537
5198 4324
8315 4370
6413 3526
6091 8980
9956 1873
6862 9170
6996 7281
2305 925
7084 6327
336 6505
846 1729
1313 5857
6124 3895
9582 545
8814 3367
5434 364
4043 3750
1087 6808
7276 7178
5788 3584
5403 2651
2754 2399
9932 5060
9676 3368
7739 12
6226 8586
8094 7539
795 570
1434 378
7467 6601
97 2902
3317 492
6652 756
7301 280
4286 9441
3865 9689
8444 6619
8440 4729
8031 8117
8097 5771
4481 675
709 8927
4567 7856
9497 2353
4586 6965
5306 4683
6219 8624
1528 2871
5732 8829
9503 19
8270 3368
9708 6715
6340 8149
7796 723
2618 2245
2846 3451
2921 3555
2379 7488
7764 8228
9841 2350
5193 1500
7034 7764
124 4914
6987 5856
3743 6491
2227 8365
9859 1936
1432 2551
6437 9228
3275 5407
1474 6121
8858 4395
6029 1237
8235 3793
5818 4428
6143 1011
5928 9529
8776 2404
4443 5763
4613 4538
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]]></test_input>
<test_output><![CDATA[141.42
212.13
726.43
593.60
416.91
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C"><![CDATA[/* 
   The proper way to do this is with Union Find, but 
   binary search works OK, too.  O(n^2 log d) where
   d is the max distance.  

   The recursive connected components implementaiton
   is a dog on Sun SPARC.
*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

int i,j,k,N,C,P;
int x[1000],y[1000];
double dsq,delta;
int mark[1000];

void set(int w, int c, double d) {
   int i,j,k;
   if (mark[w]) return;
   mark[w] = c;
   for (i=0;i<P;i++) {
      if ((x[i]-x[w])*(x[i]-x[w]) + (y[i]-y[w])*(y[i]-y[w]) < d) {
         set(i,c,d);
      }
   }
}

int try(double d) {
   int i,j,k=0;
   memset(mark,0,sizeof(mark));
   for (i=0;i<P;i++) {
      if (mark[i]) continue;
      set(i,++k,d);
   }
   return k;
}

main(){
   scanf("%d",&N);
   while (N--) {
      scanf("%d%d",&C,&P);
      for (i=0;i<P;i++) scanf("%d%d",&x[i],&y[i]);
      dsq = 100;
      for (delta = 100000000;delta > .00001; delta *=.5) {
         if (try(dsq) > C) dsq += delta;
         else dsq -= delta;
      }
      printf("%0.2lf\n",sqrt(dsq));
   }
}
]]></solution>
</item>
<item>
<title><![CDATA[Above Average]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[128]]></memory_limit>

<description><![CDATA[<p>It is said that 90% of frosh expect to be above average in their class.  You are to provide a reality check.</p>
<p>The first line of standard input contains an integer C, the number of test cases.  C data sets follow.  Each data set begins with an integer, N, the number of people in the class (1 &lt;= N &lt;= 1000). N integers follow, separated by spaces or newlines, each giving the final grade (an integer between 0 and 100)  of a student in the class.  For each case you are to output a line giving the percentage of students whose grade is above average, rounded to 3 decimal places.</p>]]></description>
<input><![CDATA[]]></input> 
<output><![CDATA[]]></output>
<sample_input><![CDATA[5
5 50 50 70 80 100
7 100 95 90 80 70 60 50
3 70 90 80
3 70 90 81
9 100 99 98 97 96 95 94 93 91
]]></sample_input>
<sample_output><![CDATA[40.000%
57.143%
33.333%
66.667%
55.556%
]]></sample_output>
<test_input><![CDATA[31
5 50 50 70 80 100
7 100 95 90 80 70 60 50
3 70 90 80
10 0 0 0 0 0 0 0 0 0 0
10 100 100 100 100 100 100 100 100 100 100
10 100 100 100 100 100 100 100 100 100 99
384 32 54 12 52 56 8 30 44 94 44 39 65 19 51 91 1 5 89 34 25 58 20 51 38 65 30 7 20 10 51 18 43 71 97 61 26 5 57 70 65 0 75 29 86 93 87 87 64 75 88 89 100 7 40 37 38 36 44 24 46 95 43 89 32 5 15 58 77 72 95 8 38 69 37 24 27 90 77 92 31 30 80 30 37 86 33 76 21 77 100 68 37 8 22 69 81 38 94 57 76 54 65 14 89 69 4 16 24 47 7 21 78 53 17 81 39 50 22 60 93 89 94 30 97 16 65 43 20 24 67 62 78 98 42 67 32 46 49 57 60 56 44 37 75 62 17 13 11 40 40 4 95 100 0 57 82 31 0 1 56 67 30 100 64 72 66 63 18 81 19 44 2 63 81 78 91 64 91 2 70 97 73 64 97 39 21 78 70 21 46 25 54 76 92 84 47 57 46 31 38 31 75 40 61 21 84 51 86 41 19 21 37 58 86 100 97 73 44 67 60 90 58 13 31 49 63 44 73 76 76 77 73 16 83 100 4 67 51 56 7 36 77 10 95 28 10 57 0 54 23 60 9 48 39 40 97 69 84 35 44 25 11 83 8 61 83 12 27 100 34 0 35 10 10 96 39 87 53 5 40 42 66 15 90 71 55 87 39 5 88 49 97 100 32 4 60 81 83 53 80 16 53 14 94 29 77 99 16 29 3 22 71 35 4 61 6 25 13 11 30 0 27 94 66 25 64 92 5 47 44 85 29 63 65 89 59 41 87 41 36 57 29 7 92 33 34 64 59 47 76 55 13 2 48 46 27 12 37 99 25 48 83 20 77 13 9 35 55 62 76 57 18 72 64 10 4 64 74 63 77 15 18 91 84
568 36 77 10 39 75 35 87 23 22 30 37 31 65 58 59 7 14 78 79 45 54 83 8 94 12 86 9 97 42 93 95 44 70 5 83 10 40 36 34 62 66 71 59 97 95 18 3 8 62 48 19 15 98 28 8 9 80 84 72 21 43 66 65 79 71 13 89 78 49 22 5 14 59 65 11 53 49 81 28 77 29 47 92 26 41 66 1 20 50 73 7 59 4 72 37 76 86 25 19 0 14 24 15 73 55 93 93 3 73 87 80 68 100 37 94 41 3 61 27 19 33 35 78 38 73 14 80 58 5 99 59 19 22 40 59 78 32 17 47 71 3 94 39 2 97 99 9 66 60 37 85 59 38 28 63 10 8 8 35 81 6 60 100 96 66 24 39 64 41 52 34 10 11 39 80 8 4 89 74 64 92 25 89 29 19 18 6 28 26 7 8 33 67 74 95 32 99 33 96 5 51 96 83 63 35 62 71 39 16 10 69 8 35 23 3 55 41 76 49 68 83 23 67 15 97 61 13 61 60 75 33 77 71 15 39 72 43 76 77 59 53 11 33 88 34 37 8 76 79 23 9 62 46 76 43 9 2 57 70 28 31 69 4 68 84 10 39 26 52 82 52 4 93 85 59 94 21 33 35 67 57 44 28 69 86 37 78 54 94 14 48 25 83 18 59 33 28 99 25 81 46 77 51 39 62 9 32 49 43 33 15 100 77 9 68 28 47 12 82 6 26 96 98 75 13 57 7 8 55 33 55 0 76 5 5 3 15 3 53 58 36 34 23 79 10 57 6 23 69 54 29 61 49 27 36 63 84 9 71 4 8 25 71 85 97 77 88 11 46 6 35 83 7 24 27 17 82 34 40 16 88 69 44 3 62 46 32 45 55 2 49 64 94 87 14 90 63 68 68 75 75 2 23 82 27 51 65 75 85 71 57 38 39 0 7 1 46 39 12 68 41 28 31 0 14 45 91 43 12 58 17 53 26 41 0 19 92 31 60 42 1 17 46 41 84 54 8 97 93 20 64 0 14 61 0 28 72 57 71 50 81 89 70 7 96 70 26 87 1 87 95 69 70 40 9 19 94 84 15 87 71 45 87 85 5 53 13 43 10 50 94 91 38 63 98 33 99 91 86 66 43 80 35 79 20 10 98 80 61 13 66 31 24 18 82 97 72 61 39 48 11 99 38 49 27 2 49 26 59 0 58 1 81 59 80 67 70 77 46 97 56 79 27 81 63 75 77 0 36 82 48 47 81 53 62 7 55 77 100 13 78 24 81 24 83 26 91 18
640 2 14 25 47 7 72 10 83 14 10 18 96 25 65 42 78 93 16 32 70 15 11 47 5 58 71 89 84 27 73 86 96 88 77 43 95 48 19 43 62 96 61 24 20 92 66 98 85 82 96 20 64 73 67 69 30 3 23 13 97 97 66 58 50 42 0 44 57 86 54 85 82 14 8 1 73 41 66 23 22 61 43 86 0 9 21 30 79 44 44 75 40 76 99 56 17 100 67 40 51 20 25 32 0 100 0 73 40 66 96 29 93 38 81 93 13 1 90 92 46 100 32 52 75 31 8 58 97 75 99 13 61 90 46 61 89 12 34 96 78 96 24 36 34 4 96 13 73 85 72 18 50 70 36 24 67 10 82 29 51 80 43 11 35 89 39 24 0 73 86 44 34 9 46 34 80 41 48 52 92 19 36 41 55 39 31 22 49 13 51 67 59 94 44 95 48 83 85 48 21 70 58 56 45 4 90 91 11 3 43 70 89 45 77 44 84 8 66 100 88 83 66 46 77 76 6 24 59 91 39 46 26 97 68 37 0 58 28 79 27 37 48 16 82 24 60 66 32 92 65 19 74 97 32 16 72 38 41 97 96 46 43 88 42 77 25 9 34 19 88 28 56 1 44 3 25 70 69 24 27 100 9 0 96 7 84 34 12 91 30 7 36 39 95 78 16 86 53 16 71 6 44 26 7 54 30 100 23 65 23 50 65 99 17 26 73 67 60 85 57 57 92 93 96 52 36 78 4 90 61 75 96 4 68 3 25 64 69 14 28 58 31 59 56 48 86 28 81 45 12 37 1 70 29 64 89 31 41 93 20 1 67 83 73 0 52 98 64 20 78 93 78 8 17 100 22 2 95 2 48 6 39 15 43 34 79 31 66 87 23 52 54 56 34 93 57 52 56 87 72 34 79 15 42 63 15 65 65 9 67 79 82 73 95 91 6 39 21 38 92 10 91 46 67 91 38 90 43 95 76 81 28 21 63 70 84 78 0 48 53 68 94 0 40 88 92 12 93 12 17 85 23 7 30 56 64 34 45 73 28 87 20 22 7 83 59 91 26 59 5 79 26 99 79 32 52 70 11 44 83 28 95 72 1 91 27 65 25 38 4 19 24 24 8 99 73 67 89 99 25 60 77 18 24 21 16 42 58 27 53 6 55 47 78 56 38 71 88 29 8 58 48 99 48 56 97 20 89 52 18 14 78 61 99 2 48 14 44 5 42 97 11 63 10 55 19 48 25 73 77 100 30 91 99 78 13 95 98 1 12 82 82 91 8 80 93 22 61 2 28 2 66 5 65 76 61 50 90 86 22 32 52 52 22 50 96 1 10 59 70 90 40 51 80 14 98 38 37 58 40 31 60 72 2 91 47 63 7 2 15 29 34 67 48 23 83 9 24 59 69 94 48 8 11 27 90 8 31 93 32 38 90 58 9 92 48 23 55 55 25
843 51 60 69 65 83 51 74 73 76 42 67 24 17 44 17 73 18 49 65 50 87 54 7 62 11 21 85 32 77 10 68 94 70 36 24 52 53 98 24 96 6 57 86 90 67 2 62 85 17 26 34 70 46 41 32 23 63 16 56 5 26 23 65 62 26 89 80 45 52 71 6 58 27 92 47 61 61 75 45 78 67 46 14 12 53 46 36 82 28 58 87 21 47 17 83 73 72 63 85 24 33 91 48 26 49 62 53 9 36 99 53 3 10 67 82 63 79 84 45 7 41 98 95 89 82 43 27 53 5 78 77 4 69 25 98 17 53 16 93 89 81 45 58 91 12 40 54 91 90 65 64 31 62 58 86 43 1 12 63 73 91 39 44 25 30 7 8 83 23 0 38 4 45 96 61 23 1 14 81 92 45 44 89 74 69 74 83 36 52 45 75 8 85 18 100 81 92 7 30 82 74 34 52 86 96 12 8 98 94 89 55 38 100 43 11 68 83 95 3 0 39 78 9 90 63 8 37 20 83 67 1 56 67 53 7 62 66 16 25 25 71 80 63 70 89 75 3 37 35 6 38 74 51 47 30 80 21 67 100 3 100 68 26 66 87 33 27 52 15 53 43 53 99 6 22 88 47 26 24 82 99 28 21 15 75 51 95 63 84 61 66 83 28 58 14 14 58 42 33 39 61 76 92 25 48 14 79 95 6 70 76 4 98 98 87 39 14 81 1 99 7 33 81 1 92 96 16 15 3 15 54 30 57 12 55 5 93 0 100 99 70 42 69 67 39 21 5 53 2 6 51 76 40 99 78 98 60 60 79 63 75 99 59 98 10 80 2 2 80 69 67 49 10 2 16 49 23 88 68 92 95 86 68 0 84 11 64 43 71 42 72 45 40 97 42 17 76 11 86 56 80 19 4 90 88 87 4 77 75 72 69 35 23 2 35 6 80 99 15 50 6 53 61 46 49 69 29 25 80 15 47 25 34 51 14 21 38 85 98 79 57 32 13 46 0 48 53 80 12 34 29 18 54 56 30 2 25 60 94 4 41 40 30 75 58 10 62 62 96 59 40 18 58 53 64 24 67 83 4 79 17 100 63 37 56 93 39 81 18 100 51 59 5 81 100 63 58 61 24 53 87 64 37 10 83 67 34 49 50 38 27 33 4 56 70 60 15 75 6 33 40 57 59 46 4 24 75 62 86 100 81 38 29 17 48 79 84 48 27 100 87 21 32 57 77 68 16 92 9 22 92 49 79 16 95 83 40 70 10 25 35 91 29 30 74 43 8 24 92 2 23 44 23 22 0 66 56 16 58 65 4 15 14 49 31 75 32 71 10 8 63 45 100 92 42 73 1 50 97 93 18 87 36 41 75 36 7 30 18 31 96 22 12 76 71 43 50 69 80 61 78 42 72 43 0 13 15 68 30 79 60 48 31 62 56 5 98 29 1 82 26 97 3 38 72 40 81 89 76 26 15 53 35 87 96 1 67 77 69 97 21 28 10 18 90 32 23 53 61 25 34 87 88 3 91 26 9 37 81 85 64 96 3 99 82 65 100 48 42 68 10 29 62 88 48 17 19 37 70 47 28 70 100 16 73 91 8 82 94 89 33 57 84 36 21 31 1 87 46 9 20 56 4 82 9 52 99 96 56 34 8 84 3 7 66 42 64 74 24 58 28 23 81 11 59 2 9 26 55 55 1 76 77 6 23 87 24 89 82 80 22 90 30 93 63 96 34 27 36 24 51 30 47 98 8 73 100 17 99 21 72 0 97 48 73 86 34 97 74 82 43 63 37 73 55 0 34 55 94 36 80 10 67 93 7 75 65 74 92 64 95 63 30 57 77 2 42 11 65 16 59 7 45 97 46 66 63 81 20 56 83 66 32 49 59 39 90 23 12 81 53 73 9
112 29 87 17 72 64 83 54 89 90 65 85 36 30 13 83 16 35 65 83 67 14 7 73 70 97 85 51 16 24 26 65 53 79 83 91 8 65 10 98 20 41 48 22 71 62 4 54 63 36 36 30 16 9 2 86 5 53 36 88 77 29 53 97 74 1 53 83 32 30 46 52 71 94 41 42 21 45 62 85 81 98 81 97 73 83 83 44 1 85 32 45 80 85 41 54 52 60 2 84 90 48 1 61 7 42 69 96 54 30 46 0 94
441 64 32 75 46 76 42 97 7 87 43 58 94 97 9 54 99 59 43 12 61 70 19 69 4 14 22 0 26 23 60 52 53 92 93 65 68 35 61 75 88 70 33 82 66 8 35 30 68 44 8 95 81 28 63 85 8 52 86 35 41 11 53 94 3 12 58 71 13 85 11 0 55 44 82 87 19 83 84 87 27 92 81 7 86 9 58 61 27 9 62 68 21 81 61 24 93 85 61 72 70 72 73 91 16 20 77 35 3 26 88 97 18 34 3 70 9 27 30 37 37 92 4 24 73 32 48 31 83 8 3 52 80 42 8 62 62 52 63 65 78 16 27 62 50 30 32 26 24 62 63 27 20 67 51 59 65 65 90 48 73 93 66 18 0 75 47 63 26 76 94 3 59 21 66 75 17 64 0 41 25 63 68 11 97 85 70 61 49 60 8 88 18 41 6 19 15 19 48 41 61 41 10 19 62 42 95 46 5 95 53 98 58 21 8 20 5 79 81 21 4 56 8 89 97 81 74 11 100 21 18 61 29 95 46 57 37 40 2 42 1 56 5 59 43 14 79 14 59 25 35 29 81 44 84 43 24 58 20 91 45 38 17 74 100 63 31 36 3 33 44 71 55 50 96 98 30 40 12 55 65 13 50 12 57 33 55 48 91 42 38 36 46 55 76 45 17 6 81 87 6 25 57 61 41 52 25 37 92 3 92 23 16 7 35 74 40 56 21 98 98 59 100 44 80 75 89 97 82 36 50 54 27 6 14 68 25 5 4 83 8 62 5 25 69 40 65 75 63 52 72 60 10 71 70 56 12 59 52 94 95 68 13 21 41 94 55 66 100 25 48 7 53 54 99 88 60 63 62 22 14 34 49 91 71 18 46 83 77 65 42 37 32 55 24 39 15 45 4 14 36 19 21 89 39 87 76 99 49 4 88 64 4 36 54 75 20 67 24 64 31 32 0 29 54 92 69 69 36 39 83 39 58 70 27 63 56 70 28 5 74 15
18 78 17 55 18 37 88 8 0 85 41 68 14 95 59 49 63 61 54
653 66 79 81 94 41 3 29 69 75 69 50 9 46 33 30 30 71 18 39 37 2 80 4 83 40 29 98 2 57 52 13 22 30 60 82 71 29 10 6 3 79 22 79 91 56 76 21 26 94 26 63 62 72 34 45 11 29 42 13 86 94 93 75 90 18 56 27 48 33 33 17 78 55 63 69 10 38 56 2 31 48 32 93 19 32 3 30 61 46 43 13 5 1 88 96 86 9 89 100 42 21 17 20 42 80 55 19 17 10 88 14 58 19 6 77 17 77 73 79 22 15 58 94 83 45 55 68 20 43 68 63 30 51 49 39 97 3 58 13 80 45 27 3 31 100 80 48 76 52 93 64 33 50 24 82 61 45 15 82 89 49 10 85 100 59 23 96 28 81 75 7 93 68 10 90 34 56 3 76 74 97 6 73 12 30 20 40 75 35 88 29 85 64 14 50 22 37 12 16 85 87 23 77 21 100 66 55 21 35 30 95 31 2 33 10 32 53 16 74 54 70 69 38 33 83 55 55 87 67 71 71 19 60 13 40 25 45 61 46 80 58 6 78 60 39 88 93 58 70 32 11 39 0 16 72 50 71 93 36 37 29 6 56 55 19 63 80 64 23 25 43 81 98 87 41 2 40 100 60 9 31 37 14 98 53 86 47 90 44 83 26 73 55 49 27 40 11 73 70 0 64 13 82 61 66 89 29 6 88 89 15 85 93 30 82 11 82 96 1 26 78 27 65 100 42 93 39 53 31 9 54 96 89 1 22 54 90 52 60 43 6 42 27 99 72 75 10 19 70 11 45 14 4 10 13 47 69 52 66 100 27 86 61 15 53 84 36 42 35 96 85 41 37 78 40 75 53 16 95 22 94 5 36 98 15 15 10 50 34 77 16 61 28 77 43 82 60 79 90 95 74 41 2 78 18 8 18 71 24 12 60 17 85 62 81 66 78 92 16 11 34 32 38 28 75 81 9 1 59 66 62 100 6 64 43 24 72 61 62 62 40 21 79 24 49 26 90 26 84 72 3 84 70 8 11 45 89 88 46 14 53 74 80 59 38 89 83 9 15 10 38 55 31 83 45 81 8 1 73 92 73 43 75 9 51 53 54 5 40 66 86 59 39 31 17 43 19 66 19 1 77 57 22 74 39 68 20 14 35 60 5 7 2 47 16 19 66 36 91 5 68 43 30 74 40 47 83 26 79 1 27 21 24 49 96 64 83 82 78 17 41 49 92 9 62 74 28 27 77 86 99 44 95 28 84 34 41 33 60 20 34 87 41 59 36 2 89 85 85 32 2 25 47 94 35 9 67 29 2 43 81 1 54 75 96 3 9 37 36 35 23 37 22 30 62 24 33 50 8 84 48 77 8 95 70 9 70 37 5 73 46 86 74 100 27 35 70 2 72 5 37 95 42 25 25 3 49 24 19 24 7 67 0 82 28 71 92 98 74 63 70 86 14 9 52 41 45 21 43 83 93 47 44
264 72 35 4 88 59 91 11 32 57 11 13 51 48 71 49 88 33 85 40 48 61 92 55 5 79 65 54 71 11 98 72 83 32 43 70 57 33 47 89 56 25 69 7 73 39 56 27 39 6 67 53 67 24 74 38 2 38 93 73 49 56 11 99 89 54 34 11 87 48 67 42 73 35 49 11 40 71 4 45 78 71 98 10 95 38 49 63 76 41 36 92 97 47 56 51 0 56 63 53 3 29 95 76 30 44 54 70 81 58 82 58 96 45 69 56 83 84 19 59 24 21 16 87 34 72 4 0 27 33 53 31 28 47 73 58 57 26 94 38 85 75 62 80 87 97 35 69 80 20 27 3 41 43 57 75 81 27 75 8 60 27 5 88 41 78 11 98 71 71 1 55 12 64 0 99 60 1 67 40 22 61 9 63 70 32 4 51 59 79 25 18 73 30 72 13 7 49 77 78 87 79 99 99 42 65 63 68 67 96 7 55 56 84 84 93 15 88 43 75 33 34 59 72 64 98 85 37 12 27 82 99 5 80 63 13 11 92 48 44 88 55 99 9 4 48 1 20 2 10 61 1 44 86 73 74 83 23 11 62 50 93 26 22 38
640 1 15 47 49 59 34 71 23 44 75 38 11 61 40 22 21 41 32 7 13 6 56 36 84 17 52 76 44 74 80 100 42 96 46 91 20 81 27 10 91 2 48 1 29 88 90 51 95 22 58 7 95 13 9 78 31 61 19 41 1 65 40 43 26 86 100 47 32 94 23 22 62 71 91 91 58 80 41 18 68 65 25 62 79 0 5 76 27 24 83 28 56 22 37 82 74 3 95 6 97 17 95 24 54 85 14 78 31 56 96 99 20 87 27 65 87 32 6 14 23 89 8 45 77 12 26 51 82 88 23 44 71 17 68 25 69 82 2 100 3 99 64 91 85 91 21 38 90 28 52 79 83 26 23 60 38 49 10 86 2 33 29 74 16 97 65 51 45 67 16 48 31 81 4 16 37 26 20 93 20 38 71 2 64 94 62 69 9 72 54 11 71 84 51 54 80 15 4 24 83 88 39 80 68 43 62 71 35 82 64 55 19 0 58 84 95 19 18 3 58 72 81 95 55 32 14 1 47 19 92 96 6 30 76 40 40 37 77 75 19 6 30 38 7 54 88 68 73 5 71 97 78 51 58 99 49 72 66 97 57 58 58 63 54 33 69 60 37 12 1 56 18 31 60 92 51 14 59 90 19 29 87 63 47 10 28 96 82 94 58 39 17 16 68 38 15 3 64 52 15 65 74 100 62 0 92 12 14 50 2 33 46 55 63 59 65 91 20 46 50 79 51 34 61 19 72 76 89 35 95 3 67 68 69 28 68 60 41 82 77 43 82 22 98 44 47 28 0 67 74 50 11 92 84 72 77 21 14 65 23 8 34 90 42 2 84 10 63 24 58 5 33 5 94 97 15 40 24 15 6 65 32 18 56 82 56 32 70 70 97 93 78 30 48 87 99 31 97 27 22 20 32 55 93 25 52 7 31 42 90 4 6 88 89 62 35 44 60 4 81 56 63 24 52 10 10 17 8 73 44 30 94 77 51 86 68 69 59 66 11 48 70 84 1 58 12 37 68 72 41 48 95 71 73 12 47 83 29 55 56 74 51 15 16 2 67 50 71 92 15 82 6 51 66 7 75 44 44 43 15 52 57 9 22 96 89 35 79 17 91 0 57 7 82 73 9 14 90 81 5 4 28 11 22 60 19 97 3 29 5 86 81 63 61 69 58 49 71 2 67 27 69 90 34 50 29 44 64 18 91 36 89 85 47 10 45 32 7 14 62 12 100 8 41 61 44 100 9 14 68 42 41 37 99 75 87 27 85 17 45 75 53 33 26 66 10 71 99 84 85 60 62 51 68 3 11 11 69 87 92 36 96 32 39 94 74 93 87 58 9 31 100 28 30 25 94 6 62 92 90 12 17 52 29 86 55 40 63 90 94 21 92 55 53 31 14 93 23 0 17 99 98 16 26 27 7 86 34 35 78 90 13 95 41 43 46 62 49 76 51
416 97 9 63 15 40 77 8 63 43 25 61 40 7 53 68 81 38 68 82 82 57 95 43 65 37 55 93 87 30 10 95 93 19 58 75 59 0 83 88 44 74 14 50 47 67 17 94 71 51 75 53 75 69 96 5 73 16 98 59 13 7 19 5 93 43 80 17 44 28 4 54 68 18 3 14 51 88 7 22 4 48 41 45 17 2 50 90 18 14 14 31 88 33 3 81 77 49 98 87 44 2 6 11 87 76 93 4 63 66 26 34 14 33 79 98 35 29 53 19 43 67 51 30 66 20 77 8 69 75 61 79 43 33 91 96 9 49 100 38 14 25 72 28 58 51 92 59 46 44 79 55 77 96 51 9 15 28 17 50 69 45 29 11 78 86 6 53 34 73 92 48 98 29 43 22 46 34 47 92 79 25 12 55 87 64 64 68 58 48 18 93 59 13 70 2 99 76 56 32 14 13 46 12 42 89 0 89 23 13 46 1 5 59 22 92 89 53 60 12 67 44 4 92 57 74 94 55 15 15 53 30 28 99 8 71 88 75 59 77 88 4 44 93 29 66 51 17 85 10 96 17 54 100 8 77 73 2 31 89 17 50 85 46 48 93 83 35 67 7 11 54 78 21 13 7 88 64 91 38 74 87 56 94 86 64 70 25 32 67 80 50 16 64 62 30 56 10 32 89 17 9 8 95 31 21 68 18 85 59 22 24 11 78 84 97 42 19 88 40 86 67 90 68 30 17 99 52 27 30 40 44 5 49 5 36 70 73 20 21 31 43 11 42 20 96 5 28 14 93 69 67 26 24 34 56 8 99 75 35 95 14 46 0 29 51 36 66 23 57 87 21 100 98 29 86 59 0 81 74 60 15 40 86 39 40 7 47 5 82 49 100 63 95 66 92 11 2 57 0 25 9 21 91 74 17 76 32 17 22 72 43 37 78 28 77 18
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1000 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
1000 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 99 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 90 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
]]></test_input>
<test_output><![CDATA[40.000%
57.143%
33.333%
0.000%
0.000%
90.000%
50.000%
49.824%
49.688%
51.839%
50.000%
51.474%
55.556%
48.392%
53.030%
51.250%
49.519%
49.486%
49.254%
50.281%
50.000%
0.000%
47.796%
51.064%
49.241%
48.993%
99.900%
0.100%
0.000%
0.000%
99.800%
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C"><![CDATA[#include <stdio.h>

int i,j,k,C,N,m[1000];
double sum,avg,cnt;

main(){
   scanf("%d",&C);
   while (C--) {
      scanf("%d",&N);
      sum = 0;
      for (i=0;i<N;i++) {
         scanf("%d",&m[i]);
         sum += m[i];
      }
      avg = sum/N;
      cnt = 0;
      for (i=0;i<N;i++) if (m[i]>avg) cnt++;
      printf("%0.3lf%%\n",100*cnt/N);
   }
}
]]></solution>
</item>
<item>
<title><![CDATA[Time Zones]]></title>
<time_limit><![CDATA[1]]></time_limit>
<memory_limit><![CDATA[128]]></memory_limit>

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]]></base64></img><description><![CDATA[<img align="right" src="http://plg1.cs.uwaterloo.ca/%7Eacm00/020928/time.gif" alt="" />
<p>Prior to the late nineteenth century, time keeping was a purely local phenomenon. Each town would set their clocks to noon when the sun reached its zenith each day. A clockmaker or town clock would be the &quot;official&quot; time and the citizens would set their pocket watches and clocks to the time of the town - enterprising citizens would offer their services as mobile clock setters, carrying a watch with the accurate time to adjust the clocks in customer's homes on a weekly basis. Travel between cities meant having to change one's pocket watch upon arrival.</p>
<p>However, once railroads began to operate and move people rapidly across great distances, time became much more critical. In the early years of the railroads, the schedules were very confusing because each stop was based on a different local time.  The standardization of time was essential to efficient operation of railroads.</p>
<p>In 1878, Canadian Sir Sanford Fleming proposed the system of worldwide time zones that we use today. He recommended that the world be divided into twenty-four time zones, each spaced 15 degrees of longitude apart. Since the earth rotates once every 24 hours and there are 360 degrees of longitude, each hour the earth rotates one-twenty-fourth of a circle or 15� of longitude. Sir Fleming's time zones were heralded as a brilliant solution to a chaotic problem worldwide.</p>
<p>United States railroad companies began utilizing Fleming's standard time zones on November 18, 1883. In 1884 an International Prime Meridian Conference was held in Washington D.C. to standardize time and select the Prime Meridian. The conference selected the longitude of Greenwich, England as zero degrees longitude and established the 24 time zones based on the Prime Meridian. Although the time zones had been established, not all countries switched immediately. Though most U.S. states began to adhere to the Pacific, Mountain, Central, and Eastern time zones by 1895, Congress didn't make the use of these time zones mandatory until the Standard Time Act of 1918.</p>
<p>Today, many countries operate on variations of the time zones proposed by Sir Fleming. All of China (which should span five time zones) uses a single time zone - eight hours ahead of Coordinated Universal Time (known by the abbreviation UTC - based on the time zone running through Greenwich at 0� longitude). Russia adheres to its designated time zones although the entire country is on permanent Daylight Saving Time and is an hour ahead of their actual zones. Australia uses three time zones - its central time zone is a half-hour ahead of its designated time zone. Several countries in the Middle East and South Asia also utilize half-hour time zones.</p>
<p>Since time zones are based on segments of longitude and lines of longitude narrow at the poles, scientists working at the North and South Poles simply use UTC time. Otherwise, Antarctica would be divided into 24 very thin time zones!</p>
<p>Time zones have recently been given standard capital-letter abbreviations as follows:</p>
<pre>
UTC Coordinated Universal Time
GMT Greenwich Mean Time, defined as UTC
BST British Summer Time, defined as UTC+1 hour
IST Irish Summer Time, defined as UTC+1 hour
WET Western Europe Time, defined as UTC
WEST Western Europe Summer Time, defined as UTC+1 hour
CET Central Europe Time, defined as UTC+1
CEST Central Europe Summer Time, defined as UTC+2
EET Eastern Europe Time, defined as UTC+2
EEST Eastern Europe Summer Time, defined as UTC+3
MSK Moscow Time, defined as UTC+3
MSD Moscow Summer Time, defined as UTC+4
AST Atlantic Standard Time, defined as UTC-4 hours
ADT Atlantic Daylight Time, defined as UTC-3 hours
NST Newfoundland Standard Time, defined as UTC-3.5 hours
NDT Newfoundland Daylight Time, defined as UTC-2.5 hours
EST Eastern Standard Time, defined as UTC-5 hours
EDT Eastern Daylight Saving Time, defined as UTC-4 hours
CST Central Standard Time, defined as UTC-6 hours
CDT Central Daylight Saving Time, defined as UTC-5 hours
MST Mountain Standard Time, defined as UTC-7 hours
MDT Mountain Daylight Saving Time, defined as UTC-6 hours
PST Pacific Standard Time, defined as UTC-8 hours
PDT Pacific Daylight Saving Time, defined as UTC-7 hours
HST Hawaiian Standard Time, defined as UTC-10 hours
AKST Alaska Standard Time, defined as UTC-9 hours
AKDT Alaska Standard Daylight Saving Time, defined as UTC-8 hours
AEST Australian Eastern Standard Time, defined as UTC+10 hours 
AEDT Australian Eastern Daylight Time, defined as UTC+11 hours 
ACST Australian Central Standard Time, defined as UTC+9.5 hours 
ACDT Australian Central Daylight Time, defined as UTC+10.5 hours 
AWST Australian Western Standard Time, defined as UTC+8 hours 
</pre>
<p>Given the current time in one time zone, you are to compute what time it is in another time zone.  The first line of input contains N, the number of test cases. For each case a line is given with a time, and 2 time zone abbreviations.   Time is given in standard a.m./p.m. format with midnight denoted &quot;midnight&quot;  and noon denoted &quot;noon&quot; (12:00 a.m. and 12:00 p.m. are oxymorons). Assuming the given time is the current time in the first time zone, give the current time in the second time zone.</p>]]></description>
<input><![CDATA[]]></input> 
<output><![CDATA[]]></output>
<sample_input><![CDATA[4
noon HST CEST 
11:29 a.m. EST GMT
6:01 p.m. CST UTC
12:40 p.m. ADT MSK
]]></sample_input>
<sample_output><![CDATA[midnight
4:29 p.m.
12:01 a.m.
6:40 p.m.
]]></sample_output>
<test_input><![CDATA[213
noon HST CEST 
11:29 a.m. EST GMT
11:30 p.m. EST GMT
10:30 p.m. ACDT UTC
10:30 a.m. ACDT UTC
3:30 a.m. NST UTC
3:30 p.m. NST UTC
8:30 p.m. NST UTC
8:30 a.m. NST UTC
midnight NDT EDT
noon NDT EDT
11:45 p.m. EST EDT
11:45 p.m. EST NST
7:30 a.m. CDT EDT
9:00 p.m. MSD CST
12:06 p.m. HST AEST
2:50 p.m. BST CDT
6:30 a.m. PDT EDT
9:33 a.m. PDT HST
11:30 a.m. CET AEST
2:50 p.m. UTC UTC
8:05 p.m. UTC UTC
6:45 p.m. PDT MSK
7:00 p.m. MSK AST
2:19 p.m. MST AST
10:06 p.m. BST AEST
11:00 a.m. CET WEST
1:20 p.m. UTC EEST
12:30 a.m. MDT EDT
9:30 a.m. WET EEST
midnight EST EET
3:59 p.m. EET AEDT
12:30 p.m. WEST ACDT
11:28 p.m. IST EDT
2:00 p.m. CST AEST
midnight EST EET
11:47 p.m. AKST AKDT
noon AEDT AWST
8:30 a.m. CDT MDT
4:00 p.m. WET AKST
8:03 p.m. PDT AKDT
4:30 a.m. MSD MSK
6:00 a.m. CDT AEST
2:48 a.m. NDT GMT
11:10 a.m. EEST ACST
noon CST MSK
6:00 p.m. MDT NST
midnight NST AST
9:00 a.m. CET IST
11:16 a.m. ADT ADT
2:30 p.m. AST MSK
12:07 a.m. AST AEST
4:52 a.m. AKST WET
6:21 a.m. AST AKST
9:44 a.m. BST MST
11:50 p.m. CST EST
8:01 p.m. MST AEDT
1:45 p.m. BST EST
noon ACDT EDT
noon MST AEST
6:55 p.m. NST AEST
5:30 p.m. MDT EEST
noon CST EST
12:30 p.m. MST CET
1:08 a.m. MDT WEST
7:06 p.m. EEST IST
5:10 a.m. AKST CDT
6:45 p.m. AST PDT
4:00 p.m. EDT AEDT
2:08 p.m. CET AKDT
noon BST MST
7:11 a.m. PST CDT
12:29 a.m. MST ADT
9:40 p.m. BST MDT
12:35 a.m. HST ADT
9:09 p.m. HST WEST
3:30 a.m. WEST PST
5:54 p.m. MSK AST
9:30 p.m. AKDT AST
4:32 p.m. AKST CST
3:00 a.m. UTC EEST
6:55 p.m. AKDT AST
9:14 a.m. AKST AST
10:30 p.m. MST HST
1:17 a.m. BST EDT
1:38 a.m. MDT UTC
9:34 a.m. UTC AEDT
noon UTC ADT
10:19 a.m. NDT EDT
1:00 a.m. PST MSK
midnight ACST ACDT
3:01 a.m. AST ACDT
1:30 p.m. MSK CEST
2:40 p.m. ADT CST
9:25 p.m. WET EST
9:30 a.m. PDT AWST
midnight EDT AEDT
7:15 a.m. NST MDT
9:22 p.m. PST ACST
10:13 p.m. ADT NDT
11:17 p.m. AWST EST
noon MSD UTC
1:00 a.m. MSD PST
11:00 p.m. CST CST
midnight EDT AST
12:23 a.m. ACDT CDT
midnight ACST IST
8:00 p.m. NST MSD
7:21 p.m. EET AST
3:32 p.m. CET CEST
1:14 a.m. CST AWST
12:04 p.m. MSD AKDT
7:02 p.m. CDT EDT
4:42 p.m. CEST ADT
7:56 a.m. GMT ADT
11:39 p.m. PST MDT
6:00 a.m. HST CST
9:59 p.m. AKDT HST
12:58 a.m. ACST EEST
midnight PDT CDT
1:00 p.m. BST NST
9:57 p.m. ADT UTC
2:41 a.m. PDT WET
12:30 a.m. EST ACDT
1:00 a.m. AWST MSK
10:00 a.m. AEST AEDT
7:40 p.m. AEST MDT
6:03 p.m. MST IST
12:19 a.m. CST WET
5:28 p.m. ACST PST
11:10 a.m. MDT EET
12:30 a.m. CET MDT
2:48 a.m. NST WET
6:36 a.m. HST BST
9:46 p.m. AKST UTC
8:15 p.m. ACST GMT
8:53 p.m. MDT MSD
8:00 a.m. MSD AEDT
5:34 a.m. CET WEST
2:41 p.m. AST MDT
2:00 a.m. AKST GMT
3:24 p.m. CEST AEST
11:00 a.m. EST AEST
6:30 a.m. PDT ADT
7:32 p.m. MSK PST
noon BST NDT
5:16 p.m. MST AEDT
5:54 p.m. ACDT PDT
12:30 a.m. NST EEST
8:15 p.m. PDT MDT
9:35 a.m. UTC IST
7:00 a.m. ACDT ADT
5:50 a.m. GMT IST
10:44 a.m. NDT UTC
7:00 a.m. CDT ACST
1:15 p.m. MSD CEST
6:00 a.m. MSK CET
11:17 a.m. WET ADT
5:30 p.m. MSK MDT
12:33 a.m. AEDT EDT
10:30 p.m. HST PDT
10:40 p.m. AWST MDT
2:37 a.m. AWST CET
5:00 p.m. ACDT ACST
midnight MSD EST
5:12 a.m. ACDT MDT
noon EDT MSD
6:00 p.m. AEST MDT
3:14 a.m. CDT CST
3:22 p.m. IST MST
10:53 p.m. MDT EDT
2:19 a.m. CDT NDT
11:22 a.m. AKDT EEST
8:00 a.m. WEST MSD
2:25 a.m. CDT EDT
noon MSD BST
1:26 p.m. AKDT AEDT
1:44 a.m. MST EST
11:30 a.m. AEDT ADT
5:05 p.m. HST ADT
11:00 a.m. NDT UTC
4:00 a.m. AST BST
6:00 p.m. AST AST
noon EST AEST
5:00 p.m. CET CDT
12:17 p.m. MSD AKDT
11:20 a.m. AST AKDT
4:30 a.m. WET CET
3:01 a.m. PST EET
4:30 a.m. NST ACST
10:12 p.m. MST CEST
3:30 a.m. WEST AKST
8:30 a.m. EST IST
11:03 a.m. HST EDT
7:00 a.m. GMT CDT
2:00 a.m. CEST CDT
5:39 a.m. ADT EST
11:01 a.m. HST AEST
8:54 p.m. EET CST
3:00 a.m. CST AKST
10:45 p.m. CST WEST
7:32 p.m. ACDT HST
noon AEST CDT
5:34 a.m. AKDT NST
12:30 a.m. EDT BST
5:57 p.m. AKST EET
7:00 p.m. AKDT EEST
2:46 p.m. HST WEST
10:55 a.m. EDT AST
2:40 p.m. MSK MDT
9:00 a.m. NST EST
6:25 p.m. AEST ACDT
10:43 p.m. CST EST
]]></test_input>
<test_output><![CDATA[midnight
4:29 p.m.
4:30 a.m.
noon
midnight
7:00 a.m.
7:00 p.m.
midnight
noon
10:30 p.m.
10:30 a.m.
12:45 a.m.
1:15 a.m.
8:30 a.m.
11:00 a.m.
8:06 a.m.
8:50 a.m.
9:30 a.m.
6:33 a.m.
8:30 p.m.
2:50 p.m.
8:05 p.m.
4:45 a.m.
noon
5:19 p.m.
7:06 a.m.
11:00 a.m.
4:20 p.m.
2:30 a.m.
12:30 p.m.
7:00 a.m.
12:59 a.m.
10:00 p.m.
6:28 p.m.
6:00 a.m.
7:00 a.m.
12:47 a.m.
9:00 a.m.
7:30 a.m.
7:00 a.m.
7:03 p.m.
3:30 a.m.
9:00 p.m.
5:18 a.m.
5:40 p.m.
9:00 p.m.
8:30 p.m.
11:30 p.m.
9:00 a.m.
11:16 a.m.
9:30 p.m.
2:07 p.m.
1:52 p.m.
1:21 a.m.
1:44 a.m.
12:50 a.m.
2:01 p.m.
7:45 a.m.
9:30 p.m.
5:00 a.m.
8:25 a.m.
2:30 a.m.
1:00 p.m.
8:30 p.m.
8:08 a.m.
5:06 p.m.
9:10 a.m.
3:45 p.m.
7:00 a.m.
5:08 a.m.
4:00 a.m.
10:11 a.m.
4:29 a.m.
2:40 p.m.
7:35 a.m.
8:09 a.m.
6:30 p.m.
10:54 a.m.
1:30 a.m.
7:32 p.m.
6:00 a.m.
10:55 p.m.
2:14 p.m.
7:30 p.m.
8:17 p.m.
7:38 a.m.
8:34 p.m.
9:00 a.m.
8:49 a.m.
noon
1:00 a.m.
5:31 p.m.
12:30 p.m.
11:40 a.m.
4:25 p.m.
12:30 a.m.
3:00 p.m.
4:45 a.m.
2:52 p.m.
10:43 p.m.
10:17 a.m.
8:00 a.m.
1:00 p.m.
11:00 p.m.
midnight
8:53 a.m.
3:30 p.m.
3:30 a.m.
1:21 p.m.
4:32 p.m.
3:14 p.m.
12:04 a.m.
8:02 p.m.
11:42 a.m.
4:56 a.m.
1:39 a.m.
10:00 a.m.
7:59 p.m.
6:28 p.m.
2:00 a.m.
8:30 a.m.
12:57 a.m.
9:41 a.m.
4:00 p.m.
8:00 p.m.
11:00 a.m.
3:40 a.m.
2:03 a.m.
6:19 a.m.
11:58 p.m.
7:10 p.m.
5:30 p.m.
6:18 a.m.
5:36 p.m.
6:46 a.m.
10:45 a.m.
6:53 a.m.
3:00 p.m.
5:34 a.m.
12:41 p.m.
11:00 a.m.
11:24 p.m.
2:00 a.m.
10:30 a.m.
8:32 a.m.
8:30 a.m.
11:16 a.m.
12:24 a.m.
7:00 a.m.
9:15 p.m.
10:35 a.m.
5:30 p.m.
6:50 a.m.
1:14 p.m.
9:30 p.m.
11:15 a.m.
4:00 a.m.
8:17 a.m.
8:30 a.m.
9:33 a.m.
1:30 a.m.
8:40 a.m.
7:37 p.m.
4:00 p.m.
3:00 p.m.
12:42 p.m.
8:00 p.m.
2:00 a.m.
2:14 a.m.
7:22 a.m.
12:53 a.m.
4:49 a.m.
10:22 p.m.
11:00 a.m.
3:25 a.m.
9:00 a.m.
8:26 a.m.
3:44 a.m.
9:30 p.m.
12:05 a.m.
1:30 p.m.
9:00 a.m.
6:00 p.m.
3:00 a.m.
11:00 a.m.
12:17 a.m.
7:20 a.m.
5:30 a.m.
1:01 p.m.
5:30 p.m.
7:12 a.m.
5:30 p.m.
2:30 p.m.
5:03 p.m.
2:00 a.m.
7:00 p.m.
3:39 a.m.
7:01 a.m.
12:54 p.m.
midnight
5:45 a.m.
11:02 p.m.
9:00 p.m.
10:04 a.m.
5:30 a.m.
4:57 a.m.
6:00 a.m.
1:46 a.m.
10:55 a.m.
5:40 a.m.
7:30 a.m.
6:55 p.m.
11:43 p.m.
]]></test_output>
<hint><![CDATA[]]></hint>
<source><![CDATA[]]></source>
<solution language="C"><![CDATA[#include <stdio.h>
#include <string.h>

char *x[] = {
"WET","0",
"UTC","0",
"GMT","0",
"BST","+1",
"IST","+1",
"WEST","+1",
"CET","+1",
"CEST","+2",
"EET","+2",
"EEST","+3",
"MSK","+3",
"MSD","+4",
"AST","-4",
"ADT","-3",
"NST","-3.5",
"NDT","-2.5",
"EST","-5",
"EDT","-4",
"CST","-6",
"CDT","-5",
"MST","-7",
"MDT","-6",
"PST","-8",
"PDT","-7",
"HST","-10",
"AKST","-9",
"AKDT","-8",
"AEST","+10",
"AEDT","+11",
"ACST","+9.5",
"ACDT","+10.5",
"AWST","+8",
"",""};

int i,j,k,h,m,n,N,time;
char buf[100];
double off;

main(){
   scanf("%d",&N);
   while (N--) {
      scanf(" %s",buf);
      if (!strcmp(buf,"noon")) time = 12*60;
      else if (!strcmp(buf,"midnight")) time = 0;
      else {
         sscanf(buf,"%d:%d",&h,&m);
         if (h == 12) h = 0;
         time = h*60 + m;
         scanf(" %s",buf);
         if (!strcmp(buf,"p.m.")) time += 12*60;
      }
      scanf(" %s",buf);
      for (i=0;*x[i] && strcmp(x[i],buf);i++);
      if (strcmp(x[i],buf)) printf("oops:  <<<%s>>>\n",buf);
      sscanf(x[i+1],"%lf",&off);
      time -= 60 * off; 
      scanf(" %s",buf);
      for (i=0;*x[i] && strcmp(x[i],buf);i++);
      if (strcmp(x[i],buf)) printf("oops:  %s\n",buf);
      sscanf(x[i+1],"%lf",&off);
      time += 60 * off; 
      time = (time + 24*60) % (24*60);
      if (time == 0) printf("midnight\n");
      else if (time == 12 * 60) printf("noon\n");
      else {
         h = time/60%12;
         if (h == 0) h = 12;
         m = time%60;
         printf("%d:%02d %s\n",h,m,time>12*60?"p.m.":"a.m.");
      }
   }
}
]]></solution>
</item>
</fps>