YSACODE discuss3

You have written on a piece of paper an array of n positive integers a[1],a[2],...,a[n] and m good pairs of integers (i₁,j₁),(i₂,j₂),...,(i_m,j_m). Each good pair (i_k,j_k) meets the following conditions: i_k+j_k is an odd number and 1≤i_k<j_k≤n.

In one operation you can perform a sequence of actions:

take one of the good pairs (i_k,j_k) and some integer v (v>1), which divides both numbers a[i_k] and a[j_k];
divide both numbers by v, i. e. perform the assignments: $\text{[math]}$ and $\text{[math]}$ .

Determine the maximum number of operations you can sequentially perform on the given array. Note that one pair may be used several times in the described operations.

Input

The first line contains two space-separated integers n, m (2≤n≤100, 1≤m≤100).

The second line contains n space-separated integers a[1],a[2],...,a[n] (1≤a[i]≤10⁹) − the description of the array.

The following m lines contain the description of good pairs. The k-th line contains two space-separated integers i_k, j_k (1≤i_k<j_k≤n, i_k+j_k is an odd number).

It is guaranteed that all the good pairs are distinct.

Output

Output the answer for the problem.

Examples

Input

Output

Input

Output

2567: Array and Operations

Description

Source/Category