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
M = 1299710
isPrime = [1]*M
isPrime[0],isPrime[1] = 0,0
for i in xrange(2,M):
    if isPrime[i]:
        for j in range(i*i,M,i):
            isPrime[j] = 0
while 1:
    n = input()
    if n==0: break
    p = q = n
    if isPrime[n]:
        print 0
    else:
        while isPrime[p]==0:p-=1
        while isPrime[q]==0:q+=1
        print q-p
    