#106Easy

Snake order

Time: 1 s · Memory: 256 MB

Statement

Print the elements of an $m \times n$ matrix in a "snake": row 1 left to right, row 2 right to left, row 3 left to right again, and so on.

The first line contains $m$ and $n$ ( $1 \le m, n \le 100$ ). Each of the next $m$ lines contains $n$ integers ( $|a_{ij}| \le 10^9$ ).

A single line with $m \cdot n$ numbers.

Input

Output

1 2 3 6 5 4 7 8 9 12 11 10

Input

2 2
1 2
3 4

Output

1 2 4 3

Choose the direction of the inner loop by the parity of the row number. In the first example: 1 2 3 6 5 4 7 8 9 12 11 10.

Snake order

Time: 1 s · Memory: 256 MB

Matrices

Print the elements of an $m \times n$ matrix in a "snake": row 1 left to right, row 2 right to left, row 3 left to right again, and so on.

The first line contains $m$ and $n$ ( $1 \le m, n \le 100$ ). Each of the next $m$ lines contains $n$ integers ( $|a_{ij}| \le 10^9$ ).

A single line with $m \cdot n$ numbers.

Input

Output

1 2 3 6 5 4 7 8 9 12 11 10

Input

2 2
1 2
3 4

Output

1 2 4 3

Choose the direction of the inner loop by the parity of the row number. In the first example: 1 2 3 6 5 4 7 8 9 12 11 10.