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>
#define MAX_N 1299709 + 1
using namespace std;

bool t[MAX_N];

bool isPrime(int x) {
  if(x == 2) return true;
  if(x < 2 || x % 2 == 0) return false;
  int i = 3;
  while(i * i <= x) {
    if(x % i == 0) return false;
    i += 2;
  }
  return true;
}

void table() {
  for(int i = 1; i < MAX_N; ++i) {
    if (isPrime(i)) t[i] = 1;
  }
}

void solve(int k) {
  int p = k, n = k;
  while(t[p] != 1) p--;
  while(t[n] != 1) n++;
  cout << n - p << endl;
}

int main() {
  table();
  int k;
  while(cin >> k && k) {
    solve(k);
  }
  return 0;
}

