B"Yura is a mathematician, and his cognition of the world is so absolute as if he have been solving formal problems a hundred of trillions of billions of years. This problem is just that! Consider all non-negative integers from the interval [0, 10^{n}) . For convenience we complement all numbers with leading zeros in such way that each number from the given interval consists of exactly n decimal digits. You are given a set of pairs (u_i, v_i) , where u_i and v_i are distinct decimal digits from 0 to 9 . Consider a number x consisting of n digits. We will enumerate all digits from left to right and denote them as d_1, d_2, ldots, d_n . In one operation you can swap digits d_i and d_{i + 1} if and only if there is a pair (u_j, v_j) in the set such that at least one of the following conditions is satisfied: We will call the numbers x and y , consisting of n digits, equivalent if the number x can be transformed into the number y using some number of operations described above. In particular, every number is considered equivalent to itself. You are given an integer n and a set of m pairs of digits (u_i, v_i) . You have to find the maximum integer k such that there exists a set of integers x_1, x_2, ldots, x_k ( 0 <= x_i < 10^{n} ) such that for each 1 <= i < j <= k the number x_i is not equivalent to the number x_j . The first line contains an integer n ( 1 <= n <= 50 ,000 ) -- the number of digits in considered numbers. The second line contains an integer m ( 0 <= m <= 45 ) -- the number of pairs of digits in the set. Each of the following m lines contains two digits u_i and v_i , separated with a space ( 0 <= u_i < v_i <= 9 ). It's guaranteed that all described pairs are pairwise distinct. Print one integer -- the maximum value k such that there ex"...