A11687 | 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 $10^{6}$ 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.