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 <cstdio>

const int MaxPrime = 1300000;

bool prime[MaxPrime];

void init_prime() {
  prime[0] = prime[1] = false;
  for (int i=2;i<MaxPrime;i++) prime[i] = true;
  for (int i=2;i<MaxPrime;i++) {
    if (!prime[i]) continue;
    for (int j=i+i;j<MaxPrime;j+=i) prime[j] = false;
  }
}

int main() {
  init_prime();
  int n;
  while (scanf("%d", &n), n!=0) {
    if (prime[n]) {
      puts("0");
      continue;
    }
    int b = n, e = n;
    while (!prime[b]) b--;
    while (!prime[e]) e++;
    printf("%d\n", e-b);
  }
  return 0;
}