**Time limit:**1.00 s**Memory limit:**512 MB

Each pair of players can play at most one game. Your task is to determine which games will be played so that everybody will be happy.

**Input**

The first input line has an integer $n$: the number of players. The players are numbered $1,2,\dots,n$.

The next line has $n$ integers $x_1,x_2,\dots,x_n$: for each player, the number of games they want to play.

**Output**

First print an integer $k$: the number of games. Then, print $k$ lines describing the games. You can print any valid solution.

If there are no solutions, print "IMPOSSIBLE".

**Constraints**

- $1 \le n \le 10^5$

- $\sum_{i=1}^{n} x_i \le 2 \cdot 10^5$

**Example**

Input:

`5`

1 3 2 0 2

Output:

`4`

1 2

2 3

2 5

3 5