Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Candies Game

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub is playing an uncommon game. Initially, he has *n* boxes, numbered 1, 2, 3, ..., *n*. Each box has some number of candies in it, described by a sequence *a*_{1}, *a*_{2}, ..., *a*_{n}. The number *a*_{k} represents the number of candies in box *k*.

The goal of the game is to move all candies into exactly two boxes. The rest of *n* - 2 boxes must contain zero candies. Iahub is allowed to do several (possible zero) moves. At each move he chooses two different boxes *i* and *j*, such that *a*_{i} ≤ *a*_{j}. Then, Iahub moves from box *j* to box *i* exactly *a*_{i} candies. Obviously, when two boxes have equal number of candies, box number *j* becomes empty.

Your task is to give him a set of moves such as Iahub to archive the goal of the game. If Iahub can't win the game for the given configuration of boxes, output -1. Please note that in case there exist a solution, you don't need to print the solution using minimal number of moves.

Input

The first line of the input contains integer *n* (3 ≤ *n* ≤ 1000). The next line contains *n* non-negative integers: *a*_{1}, *a*_{2}, ..., *a*_{n} — sequence elements. It is guaranteed that sum of all numbers in sequence *a* is up to 10^{6}.

Output

In case there exists no solution, output -1. Otherwise, in the first line output integer *c* (0 ≤ *c* ≤ 10^{6}), representing number of moves in your solution. Each of the next *c* lines should contain two integers *i* and *j* (1 ≤ *i*, *j* ≤ *n*, *i* ≠ *j*): integers *i*, *j* in the *k*th line mean that at the *k*-th move you will move candies from the *j*-th box to the *i*-th one.

Examples

Input

3

3 6 9

Output

2

2 3

1 3

Input

3

0 1 0

Output

-1

Input

4

0 1 1 0

Output

0

Note

For the first sample, after the first move the boxes will contain 3, 12 and 3 candies. After the second move, the boxes will contain 6, 12 and 0 candies. Now all candies are in exactly 2 boxes.

For the second sample, you can observe that the given configuration is not valid, as all candies are in a single box and they should be in two boxes. Also, any move won't change the configuration, so there exists no solution.

For the third sample, all candies are already in 2 boxes. Hence, no move is needed.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/14/2019 15:07:12 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|