시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB229945.000%

문제

|---|---|---|---|---|
| 1 | 1 | 3 | 5 | 1 |
|---|---|---|---|---|
| 3 | 3 | 2 | 0 | 3 |
|---|---|---|---|---|
| 3 | 0 | 3 | 2 | 3 |
|---|---|---|---|---|
| 1 | 4 | 0 | 3 | 3 |
|---|---|---|---|---|
| 3 | 3 | 3 | 1 | 1 |
|---|---|---|---|---|  (그림 1)

[그림 1]은 소수방진의 예를 보여준다. 소수방진이란 각 열, 행, 그리고 두 개의 대각선이 모두 5자리 소수로 해석되는 5x5 형태의 수의 나열을 말한다. 열은 위에서 아래로, 행은 왼쪽에서 오른쪽으로, 대각선은 둘 다 왼쪽에서 오른쪽으로 읽는다. 이러한 소수방진 중에서 다음 조건을 만족하는 것을 찾고자 한다.

  • 모든 소수들의 각 자리의 수의 합이 같아야 한다. (예제의 경우 11)
  • 가장 좌측 상단의 수는 미리 정해져있다. (예제의 경우 1)
  • 같은 소수가 한 소수방진에 두 번 이상 사용될 수 있다.
  • 가능한 답이 여러 개라면 모두 출력한다.
  • 0으로 시작하는 것은 5자리 소수로 보지 않는다. 예를 들어 00003은 5자리 소수가 아니다.

입력

입력의 첫 번째 줄에 각 소수들이 만족해야 할 각 자리의 수의 합이 주어진다.

입력의 두 번째 줄에 소수방진의 가장 좌측 상단의 수가 주어진다.

출력

가능한 소수방진을 모두 출력한다. 각 소수방진은 5줄에 걸쳐 5글자씩 출력하며, 각 소수방진 사이에는 빈 줄이 하나씩 존재한다.

예제 입력 1

11
1

예제 출력 1

11351
14033
30323
53201
13313

11351
33203
30323
14033
33311

13313
13043
32303
50231
13331
W3sicHJvYmxlbV9pZCI6IjU1MTkiLCJwcm9ibGVtX2xhbmciOiIwIiwidGl0bGUiOiJcdWMxOGNcdWMyMThcdWJjMjlcdWM5YzQiLCJkZXNjcmlwdGlvbiI6IjxwcmU+XHJcbnwtLS18LS0tfC0tLXwtLS18LS0tfFxyXG58IDEgfCAxIHwgMyB8IDUgfCAxIHxcclxufC0tLXwtLS18LS0tfC0tLXwtLS18XHJcbnwgMyB8IDMgfCAyIHwgMCB8IDMgfFxyXG58LS0tfC0tLXwtLS18LS0tfC0tLXxcclxufCAzIHwgMCB8IDMgfCAyIHwgMyB8XHJcbnwtLS18LS0tfC0tLXwtLS18LS0tfFxyXG58IDEgfCA0IHwgMCB8IDMgfCAzIHxcclxufC0tLXwtLS18LS0tfC0tLXwtLS18XHJcbnwgMyB8IDMgfCAzIHwgMSB8IDEgfFxyXG58LS0tfC0tLXwtLS18LS0tfC0tLXwgIChcdWFkZjhcdWI5YmMgMSk8XC9wcmU+XHJcblxyXG48cD5bXHVhZGY4XHViOWJjIDFdXHVjNzQwIFx1YzE4Y1x1YzIxOFx1YmMyOVx1YzljNFx1Yzc1OCBcdWM2MDhcdWI5N2MgXHViY2Y0XHVjNWVjXHVjOTAwXHViMmU0LiBcdWMxOGNcdWMyMThcdWJjMjlcdWM5YzRcdWM3NzRcdWI3ODAgXHVhYzAxIFx1YzVmNCwgXHVkNTg5LCBcdWFkZjhcdWI5YWNcdWFjZTAgXHViNDUwIFx1YWMxY1x1Yzc1OCBcdWIzMDBcdWFjMDFcdWMxMjBcdWM3NzQgXHViYWE4XHViNDUwIDVcdWM3OTBcdWI5YWMgXHVjMThjXHVjMjE4XHViODVjIFx1ZDU3NFx1YzExZFx1YjQxOFx1YjI5NCA1eDUgXHVkNjE1XHVkMGRjXHVjNzU4IFx1YzIxOFx1Yzc1OCBcdWIwOThcdWM1ZjRcdWM3NDQgXHViOWQwXHVkNTVjXHViMmU0LiBcdWM1ZjRcdWM3NDAgXHVjNzA0XHVjNWQwXHVjMTFjIFx1YzU0NFx1Yjc5OFx1Yjg1YywgXHVkNTg5XHVjNzQwIFx1YzY3Y1x1Y2FiZFx1YzVkMFx1YzExYyBcdWM2MjRcdWI5NzhcdWNhYmRcdWM3M2NcdWI4NWMsIFx1YjMwMFx1YWMwMVx1YzEyMFx1Yzc0MCBcdWI0NTggXHViMmU0IFx1YzY3Y1x1Y2FiZFx1YzVkMFx1YzExYyBcdWM2MjRcdWI5NzhcdWNhYmRcdWM3M2NcdWI4NWMgXHVjNzdkXHViMjk0XHViMmU0LiBcdWM3NzRcdWI3ZWNcdWQ1NWMgXHVjMThjXHVjMjE4XHViYzI5XHVjOWM0IFx1YzkxMVx1YzVkMFx1YzExYyBcdWIyZTRcdWM3NGMgXHVjODcwXHVhYzc0XHVjNzQ0IFx1YjljY1x1Yzg3MVx1ZDU1OFx1YjI5NCBcdWFjODNcdWM3NDQgXHVjYzNlXHVhY2UwXHVjNzkwIFx1ZDU1Y1x1YjJlNC48XC9wPlxyXG5cclxuPHVsPlxyXG5cdDxsaT5cdWJhYThcdWI0ZTAgXHVjMThjXHVjMjE4XHViNGU0XHVjNzU4IFx1YWMwMSBcdWM3OTBcdWI5YWNcdWM3NTggXHVjMjE4XHVjNzU4IFx1ZDU2OVx1Yzc3NCBcdWFjMTlcdWM1NDRcdWM1N2MgXHVkNTVjXHViMmU0LiAoXHVjNjA4XHVjODFjXHVjNzU4IFx1YWNiZFx1YzZiMCAxMSk8XC9saT5cclxuXHQ8bGk+XHVhYzAwXHVjN2E1IFx1Yzg4Y1x1Y2UyMSBcdWMwYzFcdWIyZThcdWM3NTggXHVjMjE4XHViMjk0IFx1YmJmOFx1YjlhYyBcdWM4MTVcdWQ1NzRcdWM4MzhcdWM3ODhcdWIyZTQuIChcdWM2MDhcdWM4MWNcdWM3NTggXHVhY2JkXHVjNmIwIDEpPFwvbGk+XHJcblx0PGxpPlx1YWMxOVx1Yzc0MCBcdWMxOGNcdWMyMThcdWFjMDAgXHVkNTVjIFx1YzE4Y1x1YzIxOFx1YmMyOVx1YzljNFx1YzVkMCBcdWI0NTAgXHViYzg4IFx1Yzc3NFx1YzBjMSBcdWMwYWNcdWM2YTlcdWI0MjAgXHVjMjE4IFx1Yzc4OFx1YjJlNC48XC9saT5cclxuXHQ8bGk+XHVhYzAwXHViMmE1XHVkNTVjIFx1YjJmNVx1Yzc3NCBcdWM1ZWNcdWI3ZWMgXHVhYzFjXHViNzdjXHViYTc0IFx1YmFhOFx1YjQ1MCBcdWNkOWNcdWI4MjVcdWQ1NWNcdWIyZTQuPFwvbGk+XHJcblx0PGxpPjBcdWM3M2NcdWI4NWMgXHVjMmRjXHVjNzkxXHVkNTU4XHViMjk0IFx1YWM4M1x1Yzc0MCA1XHVjNzkwXHViOWFjIFx1YzE4Y1x1YzIxOFx1Yjg1YyBcdWJjZjRcdWM5YzAgXHVjNTRhXHViMjk0XHViMmU0LiBcdWM2MDhcdWI5N2MgXHViNGU0XHVjNWI0IDAwMDAzXHVjNzQwIDVcdWM3OTBcdWI5YWMgXHVjMThjXHVjMjE4XHVhYzAwIFx1YzU0NFx1YjJjOFx1YjJlNC48XC9saT5cclxuPFwvdWw+XHJcbiIsImlucHV0IjoiPHA+XHVjNzg1XHViODI1XHVjNzU4IFx1Y2NhYiBcdWJjODhcdWM5ZjggXHVjOTA0XHVjNWQwIFx1YWMwMSBcdWMxOGNcdWMyMThcdWI0ZTRcdWM3NzQgXHViOWNjXHVjODcxXHVkNTc0XHVjNTdjIFx1ZDU2MCBcdWFjMDEgXHVjNzkwXHViOWFjXHVjNzU4IFx1YzIxOFx1Yzc1OCBcdWQ1NjlcdWM3NzQgXHVjOGZjXHVjNWI0XHVjOWM0XHViMmU0LjxcL3A+XHJcblxyXG48cD5cdWM3ODVcdWI4MjVcdWM3NTggXHViNDUwIFx1YmM4OFx1YzlmOCBcdWM5MDRcdWM1ZDAgXHVjMThjXHVjMjE4XHViYzI5XHVjOWM0XHVjNzU4IFx1YWMwMFx1YzdhNSBcdWM4OGNcdWNlMjEgXHVjMGMxXHViMmU4XHVjNzU4IFx1YzIxOFx1YWMwMCBcdWM4ZmNcdWM1YjRcdWM5YzRcdWIyZTQuPFwvcD5cclxuIiwib3V0cHV0IjoiPHA+XHVhYzAwXHViMmE1XHVkNTVjIFx1YzE4Y1x1YzIxOFx1YmMyOVx1YzljNFx1Yzc0NCBcdWJhYThcdWI0NTAgXHVjZDljXHViODI1XHVkNTVjXHViMmU0LiBcdWFjMDEgXHVjMThjXHVjMjE4XHViYzI5XHVjOWM0XHVjNzQwIDVcdWM5MDRcdWM1ZDAgXHVhYzc4XHVjY2QwIDVcdWFlMDBcdWM3OTBcdWM1MjkgXHVjZDljXHViODI1XHVkNTU4XHViYTcwLCBcdWFjMDEgXHVjMThjXHVjMjE4XHViYzI5XHVjOWM0IFx1YzBhY1x1Yzc3NFx1YzVkMFx1YjI5NCBcdWJlNDggXHVjOTA0XHVjNzc0IFx1ZDU1OFx1YjA5OFx1YzUyOSBcdWM4NzRcdWM3YWNcdWQ1NWNcdWIyZTQuPFwvcD5cclxuIiwiaGludCI6IiIsIm9yaWdpbmFsIjoiMCIsImh0bWxfdGl0bGUiOiIwIiwicHJvYmxlbV9sYW5nX3Rjb2RlIjoiS29yZWFuIn0seyJwcm9ibGVtX2lkIjoiNTUxOSIsInByb2JsZW1fbGFuZyI6IjEiLCJ0aXRsZSI6IlRoZSBQcmltZXMiLCJkZXNjcmlwdGlvbiI6IjxwcmU+XHJcbnwtLS18LS0tfC0tLXwtLS18LS0tfFxyXG58IDEgfCAxIHwgMyB8IDUgfCAxIHxcclxufC0tLXwtLS18LS0tfC0tLXwtLS18XHJcbnwgMyB8IDMgfCAyIHwgMCB8IDMgfFxyXG58LS0tfC0tLXwtLS18LS0tfC0tLXxcclxufCAzIHwgMCB8IDMgfCAyIHwgMyB8XHJcbnwtLS18LS0tfC0tLXwtLS18LS0tfFxyXG58IDEgfCA0IHwgMCB8IDMgfCAzIHxcclxufC0tLXwtLS18LS0tfC0tLXwtLS18XHJcbnwgMyB8IDMgfCAzIHwgMSB8IDEgfFxyXG58LS0tfC0tLXwtLS18LS0tfC0tLXwgIChGaWd1cmUgMSk8XC9wcmU+XHJcblxyXG48cD5GaWd1cmUgMSBzaG93cyBhIHNxdWFyZS4gRWFjaCByb3csIGVhY2ggY29sdW1uIGFuZCB0aGUgdHdvIGRpYWdvbmFscyBjYW4gYmUgcmVhZCBhcyBhIGZpdmUgZGlnaXQgcHJpbWUgbnVtYmVyLiBUaGUgcm93cyBhcmUgcmVhZCBmcm9tIGxlZnQgdG8gcmlnaHQuIFRoZSBjb2x1bW5zIGFyZSByZWFkIGZyb20gdG9wIHRvIGJvdHRvbS4gQm90aCBkaWFnb25hbHMgYXJlIHJlYWQgZnJvbSBsZWZ0IHRvIHJpZ2h0LiBVc2luZyB0aGUgZGF0YSBpbiB0aGUgSU5QVVQuVFhUIGZpbGUsIHdyaXRlIGEgcHJvZ3JhbSB0aGF0IGNvbnN0cnVjdHMgc3VjaCBzcXVhcmVzLjxcL3A+XHJcblxyXG48dWw+XHJcblx0PGxpPlRoZSBwcmltZSBudW1iZXJzIG11c3QgaGF2ZSB0aGUgc2FtZSBkaWdpdCBzdW0gKDExIGluIHRoZSBleGFtcGxlKS48XC9saT5cclxuXHQ8bGk+VGhlIGRpZ2l0IGluIHRoZSB0b3AgbGVmdC1oYW5kIGNvcm5lciBvZiB0aGUgc3F1YXJlIGlzIHByZS1kZXRlcm1pbmVkICgxIGluIHRoZSBleGFtcGxlKS48XC9saT5cclxuXHQ8bGk+QSBwcmltZSBudW1iZXIgbWF5IGJlIHVzZWQgbW9yZSB0aGFuIG9uY2UgaW4gdGhlIHNhbWUgc3F1YXJlLjxcL2xpPlxyXG5cdDxsaT5JZiB0aGVyZSBhcmUgc2V2ZXJhbCBzb2x1dGlvbnMsIGFsbCBtdXN0IGJlIHByZXNlbnRlZC48XC9saT5cclxuXHQ8bGk+QSBmaXZlIGRpZ2l0IHByaW1lIG51bWJlciBjYW5ub3QgYmVnaW4gd2l0aCB6ZXJvcywgaWUgMDAwMDMgaXMgTk9UIGEgZml2ZSBkaWdpdCBwcmltZSBudW1iZXIuPFwvbGk+XHJcbjxcL3VsPlxyXG4iLCJpbnB1dCI6IjxwPlRoZSBwcm9ncmFtIHJlYWRzIGRhdGEgZnJvbSBzdGFuZGFyZCBpbnB1dC4gRmlyc3QgdGhlIGRpZ2l0IHN1bSBvZiBwcmltZSBudW1iZXJzIGFuZCB0aGVuIHRoZSBkaWdpdCBpbiB0aGUgdG9wIGxlZnQtaGFuZCBjb3JuZXIgb2YgdGhlIHNxdWFyZS4gVGhlIGZpbGUgY29udGFpbnMgdHdvIGxpbmVzLiBUaGVyZSB3aWxsIGFsd2F5cyBiZSBhIHNvbHV0aW9uIHRvIHRoZSBnaXZlbiB0ZXN0IGRhdGEuIEluIG91ciBleGFtcGxlOjxcL3A+XHJcbiIsIm91dHB1dCI6IjxwPkluIHRoZSBzdGFuZGFyZCBvdXRwdXQsIHdyaXRlIGZpdmUgbGluZXMgZm9yIGVhY2ggc29sdXRpb24gZm91bmQsIHdoZXJlIGVhY2ggbGluZSBpbiB0dXJuIGNvbnNpc3RzIG9mIGEgZml2ZSBkaWdpdCBwcmltZSBudW1iZXIuPFwvcD5cclxuIiwiaGludCI6IiIsIm9yaWdpbmFsIjoiMSIsImh0bWxfdGl0bGUiOiIwIiwicHJvYmxlbV9sYW5nX3Rjb2RlIjoiRW5nbGlzaCJ9XQ==

출처

Olympiad > International Olympiad in Informatics > IOI 1994 > Day 1 3번