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 <vector>
#include <algorithm>
#include <numeric>

using namespace std;

#define all(c) (c).begin(), (c).end()
const int N = 1299709;

template<typename T> inline T sqr(T x){return x * x;}

void sieve(vector<int>& v, int n){
    v.assign(n, 0); iota(all(v), 2);
    for(auto div=v.begin(); sqr(*div)<=v.back(); ++div){
        v.erase(remove_if(div+1, v.end(), [&](int x){return x % *div == 0;}), v.end());
    }
}

int main(){
    vector<int> primes;
    sieve(primes, N);
    for(int k; cin >> k, k;){
        auto itr = equal_range(all(primes), k);
        cout << (*itr.second == *itr.first? *itr.second - *(--itr.first): 0) << '\n';
    }
    return 0;
}