Table Card Passing

Ported from Frontier-CS algorithmic/problems/220.

Agentics Interface

Each run executes the submitted zip_project solution once. The run command receives the case input on standard input and must write the candidate answer to standard output. The solution must not use the network during setup, build, or run.

The trusted separated evaluator compiles and runs the source-derived Frontier-CS checker against stdout.txt. Public validation contains one tiny deterministic case. Official cases, reference answers, and scoring metadata are supplied only through the required private asset official-runs.

Scoring

The primary metric is score, the average normalized Frontier-CS checker score on a 0-100 scale. Outputs rejected by the checker receive zero for that case. Official result details are score-only; public validation includes per-case feedback from the checker.

Original Statement

Playing Around the Table

Problem Description

There are n players, numbered from 1 to n sitting around a round table. The (i+1)-th player sits to the right of the i-th player for 1≤i<n, and the 1-st player sits to the right of the n-th player.

There are n^2 cards, each of which has an integer between 1 and n written on it. For each integer from 1 to n, there are exactly n cards having this number.

Initially, all these cards are distributed among all the players, in such a way that each of them has exactly n cards. In one operation, each player chooses one of his cards and passes it to the player to his right. All these actions are performed simultaneously.

Player i is called solid if all his cards have the integer i written on them. Their objective is to reach a configuration in which everyone is solid. Find a way to do it using at most (n^2−n) operations.

Input Format

The first line contains a single integer n (2≤n≤100).

Then n lines follow. The i-th of them contains n integers c1,c2,…,cn (1≤cj≤n) — the initial cards of the i-th player.

It is guaranteed that for each integer i from 1 to n, there are exactly n cards having the number i.

Output Format

In the first line print an integer k (0≤k≤(n^2−n)) — the numbers of operations you want to make.

Then k lines should follow. In the i-th of them print n integers d1,d2,…,dn (1≤dj≤n) where dj is the number written on the card which j-th player passes to the player to his right in the i-th operation.

We can show that an answer always exists under the given constraints. If there are multiple answers, print any.

Example

Input

2
2 1
1 2

Output

1
2 1

Input

3
1 1 1
2 2 2
3 3 3

Output

6
1 2 3
3 1 2
2 3 1
1 2 3
3 1 2
2 3 1

Note

In the first test case, if the first player passes a card with number 2 and the second player passes a card with number 1, then the first player has two cards with number 1 and the second player has two cards with number 2. Then, after making this operation, both players are solid.

In the second test case, 0 operations would be enough too. Note that you do not need to minimize the number of operations.

Constraints

• 2 ≤ n ≤ 100
• For each integer i from 1 to n, there are exactly n cards having the number i

Time Limit

2 seconds per test case

Memory Limit

256 MB