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>

#define rep(i, n) for(int i = 0; i < n; i++)

typedef long long ll;
using namespace std;
int mod = 1000000007;

int main(void){
    vector<int> prime(2000000, 1);
    prime[0] = 0;
    prime[1] = 0;
    for(int i = 2; i < 1500; i++){
        for(int j = (i << 1); j < 2000000; j+=i){
            prime[j] = 0;
        }
    }

    int N;
    while(true){
        cin >> N;
        if(N == 0) break;
        int l = N, r = N;
        while(prime[l] == 0) l--;
        while(prime[r] == 0) r++;
        cout << r-l << endl;
    }
    return 0;
}
