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A. Candy Bags

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGerald has *n* younger brothers and their number happens to be even. One day he bought *n*^{2} 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 *n*^{2} 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.

Input

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

Output

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 *n*^{2}. You can print the numbers in the lines in any order.

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

Examples

Input

2

Output

1 4

2 3

Note

The sample shows Gerald's actions if he has two brothers. In this case, his bags contain 1, 2, 3 and 4 candies. He can give the bags with 1 and 4 candies to one brother and the bags with 2 and 3 to the other brother.

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