You are given a sequence of n positive integers d 1 , d 2 , ..., d n ( d 1 < d 2 < ... < d n ). Your task is to construct an undirected graph such that: there are exactly d n + 1 vertices; there are no self-loops; there are no multiple edges; there are no more than 10 6 edges; its degree set is equal to d . Vertices should be numbered 1 through ( d n + 1) . Degree sequence is an array a with length equal to the number of vertices in a graph such that a i is the number of vertices adjacent to i -th vertex. Degree set is a sorted in increasing order sequence of all distinct values from the degree sequence . It is guaranteed that there exists such a graph that all the conditions hold, and it contains no more than 10 6 edges. Print the resulting graph. The first line contains one integer n ( 1 ≤ n ≤ 300 ) — the size of the degree set. The second line contains n integers d 1 , d 2 , ..., d n ( 1 ≤ d i ≤ 1000 , d 1 < d 2 < ... < d n ) — the degree set. In the first line print one integer m ( 1 ≤ m ≤ 10 6 ) — the number of edges in the resulting graph. It is guaranteed that there exists such a graph that all the conditions hold and it contains no more than 10 6 edges. Each of the next m lines should contain two integers v i and u i ( 1 ≤ v i , u i ≤ d n + 1 ) — the description of the i -th edge.