SGU 154. Factorial

154. Factorial

time limit per test: 0.5 sec.
memory limit per test: 4096 KB

input: standard input
output: standard output

You task is to find minimal natural number N, so that N! contains exactly Q zeroes on the trail in decimal notation. As you know N! = 1*2*...*N. For example, 5! = 120, 120 contains one zero on the trail.

Input

One number Q written in the input (0<=Q<=10^8).

Output

Write "No solution", if there is no such number N, and N otherwise.

Sample test(s)

Input

2

Output

10

题目大意：给出一个数n的阶乘n！的末尾0的个数，求n最小是多少，如果找不到输出No solution

思路分析：由于2和5乘积会出现0，所以可以二分一个范围，是否存在一个数末尾0的个数满足要求

#include<iostream>

using namespace std;

int cal(int n)
{
    int res=0;
    while(n)
    {
        res+=n/5;
        n/=5;
    }
    return res;
}

int main()
{
    int q;
    while(cin>>q)
    {
        if(q==0)
        {
            cout<<1<<endl;
            continue;
        }
        int right=1000000003,left=1;
        int mid;
        while(left<right)
        {
            mid=(left+right)/2;
            if(cal(mid)<q)
                left=mid+1;
            else  right=mid;
        }
        if(cal(left)==q) cout<<left<<endl;
        else cout<<"No solution"<<endl;
    }
}