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<(n);i++)

const int MAX = 1299809;
bool is_prime[MAX];
int n;


void solve() {
    int ans=0;
    int m=n;
    while(!is_prime[m]) {
        m--;
        ans++;
    }
    while(!is_prime[n]) {
        n++;
        ans++;
    }
    cout<<ans<<endl;
}

int main() {
    fill(is_prime,is_prime+MAX,true);
    is_prime[0]=is_prime[1]=false;
    for(int i=2;i<MAX;i++) {
        if(is_prime[i]) for(int j=i+i;j<MAX;j+=i) is_prime[j]=false;
    }

    while(cin>>n) {
        if(!n) return 0;
        solve();
    }

    return 0;
}