시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 214 30 23 15.646%

문제

스티브 잡숭은 남들 앞에서 발표할 때, 수학 트릭을 이용해 청중의 관심을 끌어모은다.

첫 번째로 어떤 수의 제곱근이 그 수의 절반 뒷 부분이라는 트릭 (\(\sqrt{25}=5\), \(\sqrt{5776} = 76\))을 말하고, 그 다음에는 어떤 수에 X = 2.6을 곱하면, 그 수의 첫 자리를 맨 뒷자리로 보낸 수가 된다는 트릭을 말한다. (\(135 \times 2.6 = 351\), \(270270 \times 2.6 = 702702\))

사람들은 두 번째 트릭에 열광했고, 잡숭은 X = 2.6을 제외한 다른 숫자를 찾으려고 한다.

X가 주어졌을 때, X를 곱했을 때, 결과가 원래 숫자의 첫 자리를 맨 뒷자리로 보낸 수가 되는 모든 숫자를 찾는 프로그램을 작성하시오.

입력

첫째 줄에 X (1 ≤ X < 1000)가 주어진다. X는 최대 소수점 4째 자리까지 주어진다.

출력

108보다 작은 모든 자연수 중에 X를 곱했을 때 결과가 원래 숫자의 첫 번째 자리를 맨 뒷자리로 보낸 수가 되는 모든 숫자를 한 줄에 하나씩 증가하는 순서대로 출력한다.

만약, 그러한 수가 없는 경우에는 No solution을 출력한다.

예제 입력 1

2.6

예제 출력 1

135
270
135135
270270

예제 입력 2

3.1416

예제 출력 2

No solution
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IG51bWJlcnMgaW4gYXNjZW5kaW5nIG9yZGVyLCBvbmUgbnVtYmVyIHBlciBsaW5lLiBJZiB0aGUgbGlzdCBpcyBlbXB0eSwgb3V0cHV0IGluc3RlYWQgJmxkcXVvO05vIHNvbHV0aW9uJnJkcXVvOy48XC9wPlxyXG4iLCJoaW50IjoiIiwib3JpZ2luYWwiOiIxIiwicHJvYmxlbV9sYW5nX2NvZGUiOiJcdWM2MDFcdWM1YjQifV0=