For The Lack Of A Better Title

Your have written the numbers 1, 2, ..., n on a blackboard in that order. You are given m distinct pairs of integers 1 ≤ x_i,y_i ≤ n. You can perform several operations, where in a single operation you select a given pair (x_i, y_i) and swap the x_i'th and y_i'th numbers from the left. Note that the numbers written on the blackboard at any time is a permutation of 1, 2, ..., n. Find the number of