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;    }}