The sequence of n - 1 consecutive composite numbers (positive integers that are not prime and not equal to 1) lying between two successive prime numbers p and p + n is called a prime gap of length n. For example, (24, 25, 26, 27, 28) between 23 and 29 is a prime gap of length 6.

Your mission is to write a program to calculate, for a given positive integer k, the length of the prime gap that contains k. For convenience, the length is considered 0 in case no prime gap contains k.



Input

The input is a sequence of lines each of which contains a single positive integer. Each positive integer is greater than 1 and less than or equal to the 100000th prime number, which is 1299709. The end of the input is indicated by a line containing a single zero.

Output

The output should be composed of lines each of which contains a single non-negative integer. It is the length of the prime gap that contains the corresponding positive integer in the input if it is a composite number, or 0 otherwise. No other characters should occur in the output.

Example

Input

10
11
27
2
492170
0


Output

4
0
6
0
114
#include<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
bool f[1300000];
int main(){
    fill(f,f+1300000,true);
    f[0]=f[1]=false;
    vector<int>prime(1,1);
    for(int i=2;i<=1300000;i++){
        if(!f[i])continue;
        prime.push_back(i);
        for(int j=i+i;j<=1300000;j+=i)f[j]=false;
    }

    int n;
    while(scanf("%d",&n),n){
        int pos=lower_bound(prime.begin(),prime.end(),n)-prime.begin();
        if(prime[pos]==n){
            puts("0");
        }
        else{
            printf("%d\n",prime[pos]-prime[pos-1]);
        }
    }

    return 0;
}