Gerald has n younger brothers and their number happens to be even. One day he bought n² candy bags. One bag has one candy, one bag has two candies, one bag has three candies and so on. In fact, for each integer k from 1 to n² he has exactly one bag with k candies.

Help him give n bags of candies to each brother so that all brothers got the same number of candies.

The single line contains a single integer n (n is even, 2 ≤ n ≤ 100) — the number of Gerald's brothers.

Let's assume that Gerald indexes his brothers with numbers from 1 to n. You need to print n lines, on the i-th line print n integers — the numbers of candies in the bags for the i-th brother. Naturally, all these numbers should be distinct and be within limits from 1 to n². You can print the numbers in the lines in any order.

It is guaranteed that the solution exists at the given limits.