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 <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0;i<int(n);++i)

#define N 1300000
bool prime[N];

int solve(int n){
    if(prime[n]) return 0;
    int l=n,r=n;
    while(!prime[l])l--;
    while(!prime[r])r++;
    return r-l;
}

int main(void){
    rep(i,N) prime[i] = true;
    prime[0] = prime[1] = false;
    for(int i=2; i<N; i++){
        if(!prime[i]) continue;
        for(int j=i*2; j<N; j+=i){
            prime[j] = false;
        }
    }

    int n;
    while(cin>>n,n){
        cout<<solve(n)<<endl;
    }
    return 0;
}