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

int N = 1300000;
bool is_prime[1300000];

void set_prime() {
    memset(is_prime, true, N);
    is_prime[0] = is_prime[1] = false;
    REP(i, 2, sqrt(N)) {
        if(is_prime[i]) {
            for(int j=0; i*(j+2)<N; j++) {
                is_prime[i*(j+2)] = false;
            }
        }
    }
}

int main() {
    set_prime();
    int k;
    while(1) {
        cin >> k;
        if(k == 0) break;
        if(is_prime[k]) {cout << 0 << endl; continue;}
        int l, r;
        for(l=k-1; !is_prime[l]; l--);
        for(r=k+1; !is_prime[r]; r++);
        cout << r - l << endl;
    }
}

