Team-Building

Description:

Input:

The first line contains three integers $$$n$$$, $$$m$$$ and $$$k$$$ ($$$1 \le n \le 500\,000$$$; $$$0 \le m \le 500\,000$$$; $$$2 \le k \le 500\,000$$$) — the number of students, the number of pairs of acquaintances and the number of groups respectively.

The second line contains $$$n$$$ integers $$$c_1, c_2, \dots, c_n$$$ ($$$1 \le c_i \le k$$$), where $$$c_i$$$ equals to the group number of the $$$i$$$-th student.

Next $$$m$$$ lines follow. The $$$i$$$-th of them contains two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \le a_i, b_i \le n$$$), denoting that students $$$a_i$$$ and $$$b_i$$$ are acquaintances. It's guaranteed, that $$$a_i \neq b_i$$$, and that no (unordered) pair is mentioned more than once.

Output:

Print a single integer — the number of ways to choose two different groups such that it's possible to select two teams to play the game.

Sample Input:

6 8 3
1 1 2 2 3 3
1 3
1 5
1 6
2 5
2 6
3 4
3 5
5 6

Sample Output:

2

Sample Input:

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

Sample Output:

3

Sample Input:

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

Sample Output:

0

Sample Input:

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

Sample Output:

0

Note:

The acquaintances graph for the first example is shown in the picture below (next to each student there is their group number written).

In that test we can select the following groups:

• Select the first and the second groups. For instance, one team can be formed from students $$$1$$$ and $$$4$$$, while other team can be formed from students $$$2$$$ and $$$3$$$.
• Select the second and the third group. For instance, one team can be formed $$$3$$$ and $$$6$$$, while other team can be formed from students $$$4$$$ and $$$5$$$.
• We can't select the first and the third group, because there is no way to form the teams for the game.

In the second example, we can select any group pair. Please note, that even though the third group has no students, we still can select it (with some other group) for the game.