Wężyk

Interview

Time limit1sMemory limit128 MB

Summary

Print the numbers 1 to n squared in n rows that alternate between left-to-right and right-to-left order.

Level: Easy1 of 10
Topics: Simulation, Matrix
Solved: No attempts yet

Problem

Staś's favorite game is called wężyk (a little snake). First he chooses one integer $n$ , then he starts writing consecutive natural numbers on a sheet of paper. In total he writes $n$ rows, each containing $n$ numbers.

In the first row Staś writes the numbers from $1$ to $n$ from left to right. The second row, however, he fills from right to left with the numbers from $n + 1$ to $2n$ . And so on: odd-numbered rows are filled from left to right, and even-numbered rows from right to left.

Your task is to write a program that plays wężyk automatically.

Input

The first and only line of input contains one natural number $n$ ( $1 \le n \le 100$ ).

Output

Print $n$ rows, each containing $n$ natural numbers. In total $n^2$ numbers must be printed: all natural numbers from $1$ to $n^2$ . Within each row the numbers must be separated by single spaces.

Examples3

Example 1

Input

Expected output

1 2 3 4 5 6
12 11 10 9 8 7
13 14 15 16 17 18
24 23 22 21 20 19
25 26 27 28 29 30
36 35 34 33 32 31

Example 2
Input
```
1
```
Expected output
```
1
```
Example 3
Input
```
2
```
Expected output
```
1 2
4 3
```