Open air

You are given a full set of dominoes with two numbers from 0 to N (N — is even) written on each. There is only one exemplar of each pair of numbers {a, b} It's easy to count that amount of dominoes is .

Place all dominoes horizontally in N+1 row so, that sums of numbers on dominoes in each row are equal. Guaranteed, that it's always possible.

Input

Even number N in the only line.

Output

Output N+1 line with N+2 numbers in each: a_1, b_1, a_2, b_2, ..., a_k, b_k, k = , where each pair a_i, b_{i }corresponds to a domino. Use each domino only once. Pair of numbers on each domino can be written in any order. If there are multiple solutions, you may output any one.

Limits

2 ≤ N ≤ 100, N is even.

Examples