Problem Statement

There are $N$ children, numbered $1$ to $N$.

Child $i$ has $A_i$ candies.

Your goal is to execute the following operation as few times as possible so that eventually all $N$ children have the same number of candies.

• Choose two distinct children $x,y$, and choose a positive integer $z$ not exceeding the number of candies child $x$ has. Take $z$ candies from child $x$ and give them to child $y$.

Determine whether there exists a sequence of operations such that eventually all $N$ children have the same number of candies. If it exists, find one such sequence with the minimum number of operations.

Constraints

• $2 \leq N \leq 20$
• $1 \leq A_i \leq 10^8$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 \dots A_N

Output

If there is no sequence of operations such that eventually all $N$ children have the same number of candies, output -1.

If it exists, output one with the minimum number of operations in the following format:

q
x_1 y_1 z_1
\vdots
x_q y_q z_q

Here, $q$ represents the number of operations, and $x_i,y_i,z_i$ represent the values of $x,y,z$ chosen in the $i$-th operation.

If there are multiple solutions, outputting any of them will be considered correct.