You are given an array of integers. Check whether there exists a number in this array which is divisible by all other numbers in this array. Output 1, if such a number exists, and 0 otherwise.

Input

The only line of the input contains a list of space-separated integers ai (1 ≤ ai ≤ 100) — elements of the array. The size of the array is between 2 and 10, inclusive. Note that the size of the array is not given explicitly!

Output

Output 1 if there exists element of this array which is divisible by all other elements of the array, and 0 otherwise.

Examples

Input

6 12 4


Output

1


Input

3 13


Output

0


Input

26 13 12


Output

0

Source: codeforces | Difficulty: HARD


Solutions: