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;

const int MAX_N=2e6;
vector<int> primes,is_prime(MAX_N,1);

void sieve(){
    is_prime[0]=is_prime[1]=0;
    for (int i=2;i<MAX_N;++i){
        if (is_prime[i]){
            primes.emplace_back(i);
            for (int j=2*i;j<MAX_N;j+=i) is_prime[j]=0;
        }
    }
}

int k,ans;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    sieve();
    while(cin >> k,k){
        if (is_prime[k]){
            cout << 0 << '\n';
            continue;
        }
        auto itr=upper_bound(primes.begin(),primes.end(),k);
        ans=*itr-*(itr-1);
        cout << ans << '\n';
    }
}
