Klee is developing a new type of bomb called Peng Peng Bomb!
There are bombs numbered from to , bomb has color . The bombs are connected with links, each link connects two different bombs. Bomb will explode if meets one of the following conditions:

• is on fire by Klee.
• Bomb connected to and of the same color as explodes. Formally, there exists a link between and , and holds.

Klee can choose exact 1 bomb to be on fire. You can change at most 1 bomb and recolor it (i.e. change to any color you want).

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

输入描述:

The first line of input contains two integers  and  --- the number of bombs and links respectively.
The second line contains  integers  --- the color of each bomb.
In the next  lines, each line contains two integers  --- two bombs which is connected by the link.
It is guaranteed that for any pair of bombs , there are at most  link between them.

输出描述:

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

5 3
1 1 2 1 2
1 2
2 3
3 4

4

In the example , if you change  to  and Klee choose any one of  to be on fire,  bombs will explode.

4 6
1 2 1 2
1 2
2 3
3 4
4 1
1 3
2 4

3