프로그램 명: dilemma
제한시간: 1 초

[문제요약] 입력으로 주어진 수 N 이 3 자리수 abc 이면

2^e = abc.....
최소 e 을 찾는 것이문제이다. 단 주어진 입력의 자리수 보다 찾고자 하는 수는 2 배 보다 크다. 세자리 수 abc 이면 찾고자 하는 수는 7 자리 이상이다.

찾고자 하는 수가 없다면 "no power of 2"를 출력한다.

An archeologist seeking proof of the presence of extraterrestrials in the Earth's past, stumbles upon a partially destroyed wall containing strange chains of numbers.

The left-hand part of these lines of digits is always intact, but unfortunately the right-hand one is often lost by erosion of the stone. However, she notices that all the numbers with all its digits intact are powers of 2, so that the hypothesis that all of them are powers of 2 is obvious. To reinforce her belief, she selects a list of numbers on which it is apparent that the number of legible digits is strictly smaller than the number of lost ones, and asks you to find the smallest power of 2 (if any) whose first digits coincide with those of the list.

Thus you must write a program such that given an integer, it determines (if it exists) the smallest exponent E such that the first digits of 2E coincide with the integer (remember that more than half of the digits are missing).

입력

It is a set of lines with a positive integer N not bigger than 2147483648 in each of them.

출력

For every one of these integers a line containing the smallest positive integer E such that the first digits of 2E are precisely the digits of N, or, if there is no one, the sentence ``no power of 2".

입출력 예

입력

1
2
10

출력

7
8
20

출처: Miguel A. Revilla 2000-02-09
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