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
import java.util.*;class Main{public static void main(String[]z){Scanner s=new Scanner(System.in);int i=0,e=2,x=195,y;int[]p=new int[x];for(;i<x;p[i++]=e++)for(;f(p,e)<1;e++);for(;(x=y=s.nextInt())>0;System.out.println(x-y)){for(;f(p,x)<1;++x);for(;f(p,y)<1;--y);}}static int f(int[]s,int n){for(int e:s)if(e>0&&n!=e&&n%e<1)return 0;return 1;}}