You are hired by French NSA to break the RSA code used on the Pink Card. The easiest way to do that is to factor the public modulus and you have found the fastest algorithm to do that, except that you have to solve a subproblem that can be modeled in the following way.

Let P = {p₁, p₂ ... p_n} be a set of prime numbers. If S = {s₁, s₂... s_u} and T = {t₁ ... t_v} are formed with elements of P, then S*T will denote the quantity s₁ * s₂ * ... * s_u * t₁ * t₁ * ... t_v.

We call relation a set of two primes p, q, where p and q are distinct elements of P. You dispose of a collection of R relations S_i = {p_i, q_i} and you are interested in finding sequences of these S_i1, S_i2 ... S_ik such that S_i1 * S_i2 * ... * S_ik is a perfect square.

The way you look for these squares is the following. The ultimate goal is to count squares that appear in the process. Relations arrive one at a time. You maintain a collection of C relations that do not contain any square subproduct. This is easy: at first, C is empty. Then a relation arrives and C begins to grow. Suppose a new relation {p, q} arrives. If no square appears when adding {p, q} to C, then {p, q} is added to the collection. Otherwise, a square is about to appear, we increase the number of squares, but we do not store this relation, hence C keeps the desired property.

Let us consider an example. First arrives S₁ = {2, 3} and we put it in C. Then arrives S₂ = {5, 11}, S₃ = {3, 7} and they are stored in C. Now enters the relation S₄ = {2, 7}. This relation could be used to form the square: S₁ * S₃ * S₄ = (2 * 3) * (3 * 7) * (2 * 7) = (2 * 3 * 7)².

So we count 1 and do not store S₄ in C. Now we consider S₅ = {5, 11} that could make a square with S₂, so we count 1 square more. Then S₆ = {2, 13} is put into C. Now C could make the square S₁ * S₃ * S₆ * S₇. Eventually, we get 3 squares.

Input

The first line of the input contains a number T ≤ 30 that indicates the number of test cases to follow. Each test case begins with a line containing two integers P and R: P ≤ 10⁵ is the number of primes occurring in the test case; R (≤ 10⁵) is the number of sets of primes that arrive. The subsequent R lines each contain two integers i and j making a set {p_i,q_i} (1 ≤ i, j ≤ P). Note that we actually do not deal with the primes, they are irrelevant to the solution.

Output

For each test case, output the number of squares that can be formed using the preceding rules.

Example

Input:
2
6 7
1 2
3 5
2 4
1 4
3 5
1 6
4 6
2 3
1 2
1 2
1 2

Output:
3
2