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 math
def sieve (n):
	prime = [0,0]
	prime += [1 for i in range(n-1)]
	ub = math.sqrt(n) + 1
	d = 2
	while d <= ub:
		if prime[d] == 0:
			d += 1
			continue
		prod = 2
		while d * prod <= n:
			prime[d*prod] = 0
			prod += 1
		d += 1
	return prime
prime = sieve(1299709)
while 1:
	k = int(raw_input())
	if k == 0:
		break
	l = r = k
	while prime[l] == 0:
		l -= 1
	while prime[r] == 0:
		r += 1
	print (r-1) - (l+1) + 2