Candy Bags

读懂了题就会发现这是个超级大水题

Description

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.

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 n². You can print the numbers in the lines in any order.

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

Sample Input

Input

2

Output

1 4
2 3

Hint

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.

#include<iostream>
#include<cstring>
#include<cstdio>
#include<stack>
using namespace std;
int main()
{
    int N;
    int a[];

    scanf("%d",&N);
    int l=;
    int r=N*N;

    while(l<r)
    {
        cout<<l<<" "<<r<<endl;
        l++;
        r--;
    }
}