The ICPC is an organization made up of lots of competitive programmers, but it's very chaotic, so you have been tasked with assigning a command chain. A command chain can be seen as a directed graph where the vertex ($$$i,j$$$) indicates that the $$$i$$$-th competitive programmer can give orders to the $$$j$$$-th competitive programmer.
You know competitive programmers are very egotistical people, so they will be mad unless they have power over at least $$$a_{i}$$$ people (this number can be different for each person). But if they have control over more than $$$a_{i}$$$ persons, they will go mad with power, so you want to make the command chain so that every person has control over exactly $$$a_{i}$$$ persons. You also don't want to have a cycle, that means, a path following the edges of the graph, such that you begin and end on the same person.
We say a person $$$i$$$ has power over a person $$$j$$$ if there is a sequence of people $$$b_{1},b_{2},\ldots,b_{k}$$$ such that $$$b_{1}=i$$$, $$$b_{k}=j$$$, and $$$b_{h}$$$ can give orders to $$$b_{h+1}$$$ for all $$$1\leq h \lt k$$$. Notice that a person always has power over itself.
To save resources, and so it is not that complicated, you can use at most $$$10^{6}$$$ edges on your graph.
The first line of input contains an integer $$$N$$$ ($$$1 \leq N \leq 10^{5}$$$) — The number of people in the organization.
The second line of input contains $$$N$$$ integers $$$a_{i}$$$ ($$$1 \leq a_i \leq N$$$) ($$$a_{1}+a_{2}+\ldots+a_{N}\leq 10^{6}$$$) — The $$$i$$$-th integer is the number of people that the $$$i$$$-th programmer must have power over.
If it's impossible to create the command chain with the restrictions of the problem, print -1.
Otherwise, print $$$m$$$ — The number of edges in your graph. On the next $$$m$$$ lines print two integers $$$u_{i}$$$ and $$$v_{i}$$$ indicating that $$$u_{i}$$$ can give orders to $$$v_{i}$$$.
It can be proven that with the conditions of the problem, it is possible to construct the graph with at most $$$10^{6}$$$ edges.
55 1 1 1 1
4 1 2 1 3 1 4 1 5
55 5 5 5 5
-1
