URAL 1385 Interesting Number

Description

Tyomitch calls the number with 2 N digits (without leading zeroes) "interesting", if it's divisible by both the number formed from its firstN digits and the number formed from its last N digits. For example, 1020 is "interesting" (divisible by 10 and 20) and 2005 is not. Tyomitch wants to know how many "interesting" 2 N-digit numbers exist. You are to help him.

Input

Input contains an integer N (1 ≤ N ≤ 10000).

Output

Output the number of "interesting" 2 N-digit numbers.

Sample Input

inputoutput

1

14

Notes

11, 12, 15, 22, 24, 33, 36, 44, 48, 55, 66, 77, 88, 99.

脑洞题。。打表可以看出来大致的规律。

还有一种方法 

把这个数写成 a*10^n+b,则满足条件等价于b%a=0 and a*10^n%b=0，令 b=ka，则10^n%c=0。且a和b都是n位数。

当 n==1 c可为 1 2 5；当 n==2 c可为 1 2 4 5；n>=3 c可为1 2 4 5 8.

当a为n位数时，要控制a的范围保证b也是n位数。显然，n==1 ans=14,n==2 ans=155

n>=3时，令 a = 10^(n+1)

则(a/8-a/10)*5+(a/5-a/8)*4+(a/4-a/5)*3+(a/2-a/4)*2+(a-a/2)*5=63/40*(10^n)

#include <iostream>#include <stdio.h>#include <string>#include <cstring>#include <cmath>#include <algorithm>using namespace std;int n;int main(){    while(~scanf("%d",&n))    {        if(n==1) cout<<14<<endl;        else if(n==2) cout<<155<<endl;        else        {            cout<<1575;            for(int i=0;i<n-3;i++)            cout<<0;            cout<<endl;        }    }    return 0;}