B"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: The Hamming distance H(a, xe2 x80 x89b) between two strings a and b of length n is the number of positions at which the corresponding symbols are different. xd0 xa1hris 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, xe2 x80 x89b) xe2 x80 x89+ xe2 x80 x89H(b, xe2 x80 x89c) xe2 x80 x89+ xe2 x80 x89H(c, xe2 x80 x89a) is maximal among all the string triples constructed from the dreamed strings. Help Chris wake up from this nightmare! The first line of input contains two space-separated integers n and m (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89109; 3 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89m xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89105), 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 si and fi (0 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89si xe2 x80 x89 xe2 x89 xa4 xe2 x80 x891; 1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89fi xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n), the description of the string with index i; that means that the first fi bits of the i-th string are equal to si, and the remaining n xe2 x80 x89- xe2 x80 x89fi bits are equal to 1 xe2 x80 x89- xe2 x80 x89si. There can be multiple equal strings in Chris's dream. 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."...