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;


int main(void){
    vector<bool> array(1299800, true);

    for(int i = 2; i < 1299750; i++){
        if(array[i] == true){
            for(int j = 2*i; j < 1299750; j += i){
                array[j] = false;
            }
        }
    }

    while(1){
        int n; cin >> n;
        if(n == 0) break;
        int up = n, down = n;
        
        while(1){
            if(array[up] == true) break;
            up++;
        }

        while(1){
            if(array[down] == true) break;
            down--;
        }

        cout << up - down << endl;
    }

    return 0;
}