Problem Setting

문제

Farmer John created $NN$ ($1\le N\le {10}^{5}1\backslash le\; N\backslash le\; 10^5$) problems. He then recruited $MM$ ($1\le M\le 201\backslash le\; M\backslash le\; 20$) test-solvers, each of which rated every problem as "easy" or "hard."

His goal is now to create a problemset arranged in increasing order of difficulty, consisting of some subset of his $NN$ problems arranged in some order. There must exist no pair of problems such that some test-solver thinks the problem later in the order is easy but the problem earlier in the order is hard.

Count the number of distinct nonempty problemsets he can form, modulo ${10}^9+710^9+7$.

입력

The first line contains $NN$ and $MM$.

The next $MM$ lines each contain a string of length $NN$. The $ii$th character of this string is E if the test-solver thinks the $ii$th problem is easy, or H otherwise.

출력

The number of distinct problemsets FJ can form, modulo ${10}^9+710^9+7$.