CF976D.Degree Set

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 106 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 106 edges.

Print the resulting graph.

给你一个长度为 $n$ 的正整数序列 $d_1,\,d_2,\,...,\,d_n$（满足 $d_1 < d_2 < \dots < d_n$）。你的任务是构造一个无向图，使其满足以下条件：

• 图中恰好有 $d_n + 1$ 个顶点；
• 图中不存在自环；
• 图中不存在重边；
• 图中的边数不超过 $10^6$；
• 图的度集（degree set）恰好等于序列 $d$。

顶点编号应为 $1$ 到 $d_n + 1$。

度序列（degree sequence）是一个长度等于图中顶点数的数组 $a$，其中 $a_i$ 表示与第 $i$ 个顶点相邻的顶点个数。

度集（degree set）是将度序列中所有互不相同的值按升序排列后得到的序列。

题目保证：存在满足上述所有条件的图，且其边数不超过 $10^6$。

请输出所构造的图。

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.

第一行包含一个整数 $n$（$1 \leq n \leq 300$）—— 度数集合的大小。

第二行包含 $n$ 个整数 $d_1, d_2, \ldots, d_n$（$1 \leq d_i \leq 1000$，且 $d_1 < d_2 < \ldots < d_n$）—— 度数集合。

In the first line print one integer m (1 ≤ m ≤ 106) — 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 106 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.

第一行输出一个整数 $m$（$1 \leq m \leq 10^6$）—— 表示所构造图中的边数。保证存在满足所有条件的图，且其边数不超过 $10^6$。

接下来的 $m$ 行中，每行应包含两个整数 $v_i$ 和 $u_i$（$1 \leq v_i,\, u_i \leq d_n + 1$）—— 描述第 $i$ 条边。