K. Klee and Bomb
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Klee is developing a new type of bomb called Peng Peng Bomb!

There are $$$n$$$ bombs numbered from $$$1$$$ to $$$n$$$, bomb $$$i$$$ has color $$$c_i$$$. The $$$n$$$ bombs are connected with $$$m$$$ links, each link connects two different bombs. Bomb $$$x$$$ will explode if meets one of the following conditions:

  • $$$x$$$ is on fire by Klee.
  • Bomb $$$y$$$ connected to $$$x$$$ and of the same color as $$$x$$$ explodes. Formally, there exists a link between $$$x$$$ and $$$y$$$, and $$$c_x = c_y$$$ holds.
Klee can choose exact 1 bomb to be on fire. You can change at most 1 bomb $$$x$$$ and recolor it (i.e. change $$$c_x$$$ to any color you want).

Please help Klee find the maximum number of bombs can be exploded.

Input

The first line of input contains two integers $$$n(1\le n\le 3\times 10^5)$$$ and $$$m(0\le m\le 3\times 10^5)$$$ — the number of bombs and links respectively.

The second line contains $$$n$$$ integers $$$c_1, c_2, \dots, c_n(1\le c_i\le n)$$$ — the color of each bomb.

In the next $$$m$$$ lines, each line contains two integers $$$u, v(1\le u,v\le n, u\ne v)$$$ — two bombs which is connected by the link.

It is guaranteed that for any pair of bombs $$$(x, y)$$$, there are at most $$$1$$$ link between them.

Output

You should output an integer — the maximum number of bombs can be exploded.

Examples
Input
5 3
1 1 2 1 2
1 2
2 3
3 4
Output
4
Input
4 6
1 2 1 2
1 2
2 3
3 4
4 1
1 3
2 4
Output
3
Note

In the example $$$1$$$, if you change $$$c_3$$$ to $$$1$$$ and Klee choose any one of $$$[1,2,3,4]$$$ to be on fire, $$$4$$$ bombs will explode.