Friendship Assignment

There are N people, and the i^th person wants to have $G_i$ friends. Each friendship is mutual. Your task is to assign friendships between these people such that for every person i, the number of friends they have is exactly $G_i$. If such an assignment exists, output the list of friendship pairs; otherwise, output -1.

Note: Each edge (i, j) increases the friend count for both person i and person j, and each pair is counted only once.

inputFormat

The first line contains a single integer $N$, the number of people.
The second line contains $N$ integers $G_1, G_2, \ldots, G_N$, where $G_i$ is the number of friends person i wants.

outputFormat

If a valid friendship assignment exists, first output an integer $M$, the number of friendship pairs, followed by $M$ lines each containing two integers (1-indexed) representing a pair of friends. Otherwise, output -1.

sample

4
1 2 1 0

2
2 1
2 3