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

 

 

[submit]

[forum]

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Author:	Andrew V. Lazarev
Resource:	Saratov Subregional School Team Contest, 2002
Date:	Spring, 2002

#include <iostream>
#include <cstdio>

using namespace std;

int main()
{
    int q;
    while(cin>>q)
    {
        int i,ans,high=2000000000,low=1,mid;
        if(q==0) { puts("1"); continue;}
        while(low<=high)
        {
            mid=(low+high)>>1;
            int k=1,cnt=0;
            for(i=1;k<=mid;i++)
            {
                k=k*5;
                cnt+=mid/k;
            }
            if(cnt>=q)
            {
                high=mid-1;
            }
            else if(cnt<q)
            {
                low=mid+1;
            }
        }
        int tek=max(low,max(high,mid));
        int Q=0,k=1;
        for(i=1;k<=tek;i++)
        {
            k=k*5;
            Q+=tek/k;
        }
        if(Q==q) printf("%d
",tek);
        else puts("No solution");
    }
    return 0;
}

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