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 MAXN = 1300000;
int isP[MAXN];
vector<int> Prime, rPrime;

int main() {
  memset(isP, -1, sizeof(isP));
  isP[0] = isP[1] = false;
  for(int i = 2; i < MAXN; ++i) {
    if(!isP[i]) continue;
    Prime.push_back(i);
    for(int j = i*2; j < MAXN; j += i) isP[j] = false;
  }
  rPrime = Prime;
  reverse(rPrime.begin(), rPrime.end());
  for(int n; cin >> n && n;) {
    int a = *lower_bound(rPrime.begin(), rPrime.end(), n, greater<int>());
    int b = *lower_bound(Prime.begin(), Prime.end(), n);
    if(a == n || b == n) cout << 0 << endl;
    else cout << b - a << endl;
  }
  return 0;
}