Little Chris is having a nightmare. Even in dreams all he thinks about is math.

Chris dreams about m binary strings of length n, indexed with numbers from 1 to m. The most horrifying part is that the bits of each string are ordered in either ascending or descending order. For example, Chris could be dreaming about the following 4 strings of length 5:

$\text{[math]}$

The Hamming distance H(a, b) between two strings a and b of length n is the number of positions at which the corresponding symbols are different.

Сhris thinks that each three strings with different indices constitute a single triple. Chris's delusion is that he will wake up only if he counts the number of such string triples a, b, c that the sum H(a, b) + H(b, c) + H(c, a) is maximal among all the string triples constructed from the dreamed strings.

Help Chris wake up from this nightmare!

Input

The first line of input contains two space-separated integers n and m (1 ≤ n ≤ 10⁹; 3 ≤ m ≤ 10⁵), the length and the number of strings. The next m lines contain the description of the strings. The i-th line contains two space-separated integers s_i and f_i (0 ≤ s_i ≤ 1; 1 ≤ f_i ≤ n), the description of the string with index i; that means that the first f_i bits of the i-th string are equal to s_i, and the remaining n - f_i bits are equal to 1 - s_i. There can be multiple equal strings in Chris's dream.

Output

Output a single integer, the number of such string triples among the given that the sum of the Hamming distances between the strings of the triple is maximal.

Hamming Triples

Examples