There are 3 kinds of animals A, B and C. A can eat B, B can eat C, C can eat A. It's interesting, isn't it?

Now we have n animals, numbered from 1 to n. Each of them is one of the 3 kinds of animals: A, B, C.

Today Mary tells us k pieces of information about these n animals. Each piece has one of the two forms below:

• 1 x y: It tells us the kind of x and y are the same.
• 2 x y: It tells us x can eat y.

Some of these k pieces are true, some are false. The piece is false if it satisfies one of the 3 conditions below, otherwise it's true.

• X or Y in this piece is larger than n.
• This piece tells us X can eat X.
• This piece conflicts to some true piece before.

Input

The first line contains a single integer t. t blocks follow.

For every block, the first line contains two integers n (1 <= n <= 50000) and k (1 <= k <= 100000). k lines follow, each contains 3 positive integers D (1 <= D <= 2), X, Y, separated by single spaces.

Output

Output t lines, each contains a single integer - the number of false pieces in the corresponding block.

Example

Input:
1
100 7
1 101 1
2 1 2
2 2 3
2 3 3
1 1 3
2 3 1
1 5 5

Output:
3

Hint

The false pieces are the 1st, the 4th and the 5th ones.