Array Rotation 1

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Time limit1sMemory limit512 MB

Summary

Rotate each concentric ring of an N by M matrix counterclockwise R times, then print the resulting matrix.

Level: Medium5 of 10
Topics: Matrix, Simulation, Implementation, Array
Solved: No attempts yet

Problem

Given an array of size N×M, we want to rotate it. The array must be rotated counterclockwise as shown below.

A[1][1] ← A[1][2] ← A[1][3] ← A[1][4] ← A[1][5]
   ↓                                       ↑
A[2][1]   A[2][2] ← A[2][3] ← A[2][4]   A[2][5]
   ↓         ↓                   ↑         ↑
A[3][1]   A[3][2] → A[3][3] → A[3][4]   A[3][5]
   ↓                                       ↑
A[4][1] → A[4][2] → A[4][3] → A[4][4] → A[4][5]

Given an array and an integer R, find the result of rotating the array R times.

Input

The first line gives the array dimensions N and M and the number of rotations R to perform.

The next N lines give the elements Aij of array A.

Output

Print the result of rotating the given array R times.

Constraints

2 ≤ N, M ≤ 300
1 ≤ R ≤ 1,000
min(N, M) mod 2 = 0
1 ≤ Aij ≤ 10^8

Examples3

Example 1

Input

4 4 2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Expected output

Example 2

Input

5 4 7
1 2 3 4
7 8 9 10
13 14 15 16
19 20 21 22
25 26 27 28

Expected output

28 27 26 25
22 9 15 19
16 8 21 13
10 14 20 7
4 3 2 1

Example 3
Input
```
2 2 3
1 1
1 1
```
Expected output
```
1 1
1 1
```