Description

There are $N$ people who want to make friends with each other. Person $i$ wants to make friends with $G_i$ people.

Find one feasible assignment of friendships.

Input Format

The first line contains an integer $N$, representing the number of people.
The next $N$ lines each contain an integer $G_i$, meaning that person $i$ wants to make friends with $G_i$ people.

Output Format

If there is no solution, output NO SOLUTION in one line.
If there is a solution, first output SOLUTION in one line.
Then output $N$ lines, where line $i$ contains $G_i$ integers, indicating with which people person $i$ makes friends.

Note that in any solution, the $G_i$ integers in line $i$ must be output in increasing order.
If there are multiple solutions, output any one of them.

3
1
2
1 

SOLUTION
2
1 3
2 

3
2
2
1 

NO SOLUTION

Hint

Constraints

For $100\%$ of the testdata, $2 \le N \le 1000$, $1 \le G_i < N$.

This problem uses Special Judge.

Notes

Translated from BalticOI 2002 Day1 B Tennis Club。

Translated by ChatGPT 5