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>
using namespace std;int X, Y, A, i, j;
int main(){while (true){cin>>A;if(A==0){break;}
for(i=A;i>=2;i--){for(j=2;j*j<=i;j++){if(i%j==0){goto E;}}X=i;goto F;E:;}
F:;for(i=A;i<(1<<27);i++){for(j=2;j*j<=i;j++){if(i%j==0){goto G;}}Y=i;goto H;G:;}
H:; cout<<Y-X<<endl;}}