Codeforces Round 284 (Div. 1) |
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Finished |

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number theory

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C. Array and Operations

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 (*i*_{1}, *j*_{1}), (*i*_{2}, *j*_{2}), ..., (*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: and .

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*] ≤ 10^{9}) — 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

3 2

8 3 8

1 2

2 3

Output

0

Input

3 2

8 12 8

1 2

2 3

Output

2

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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