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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;

vector<bool> prime(1300000, true);

int main(){
    prime[0]=prime[1]=false;
    for(int i=2; i*i<1300000; i++){
        if(prime[i]){
            for(int j=2; i*j<1300000; j++){
                prime[i*j] = false;
            }
        }
    }
    
    while(1){
        int n;
        cin >> n;
        if(n==0) break;

        int min=n,max=n;
        while(!prime[min]) min--;
        while(!prime[max]) max++;
        cout << max-min << endl;
    }
    return 0;
}