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 <cstring>
using namespace std;

#define MAX_N 1299709+1

bool prime[MAX_N];

void init() {
    memset(prime, 1, sizeof(prime));
    prime[0] = prime[1] = false;
    for (int i = 2; i <= MAX_N; i++) 
        if (prime[i]) 
            for (int j = i+i; j <= MAX_N; j+=i) 
                prime[j] = false;
}

int main() {
    init();
    int n;
    while (cin >> n, n != 0) {
        int lb = n;
        int ub = n;
        while (!prime[lb]) 
            lb--;
        while (!prime[ub])
            ub++;
        cout << ub - lb << endl;
    }
    return 0;
}