Problem: 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.

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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long int MOD = 1000000007;
const long double PI = 2 * acos(0.0);
const vector<long long int> dx = {1, -1, 0, 0};
const vector<long long int> dy = {0, 0, 1, -1};
vector<long long int> ga(long long int n, bool oneIndexed = false) {
  vector<long long int> a;
  if (oneIndexed) a.push_back(0ll);
  for (long long int i = 0; i < n; i++) {
    long long int p;
    cin >> p;
    a.push_back(p);
  }
  return move(a);
}
vector<unsigned long long int> gau(unsigned long long int n,
                                   bool oneIndexed = false) {
  vector<unsigned long long int> a;
  if (oneIndexed) a.push_back(0llu);
  for (unsigned long long int i = 0; i < n; i++) {
    unsigned long long int p;
    cin >> p;
    a.push_back(p);
  }
  return move(a);
}
vector<string> gas(unsigned long long int n, bool oneIndexed = false) {
  vector<string> a;
  if (oneIndexed) a.push_back("");
  for (unsigned long long int i = 0; i < n; i++) {
    string p;
    cin >> p;
    a.push_back(p);
  }
  return move(a);
}
template <typename T, typename A>
void pa(vector<T, A> const &a, long long int begin = 0,
        long long int end = -1) {
  if (end == -1) end = (long long int)a.size() - 1;
  for (long long int i = begin; i <= end; i++) {
    cout << a[i] << " ";
  }
  cout << "\n";
}
template <typename T, typename A>
void papair(vector<T, A> const &a, long long int begin = 0,
            long long int end = -1) {
  if (end == -1) end = (long long int)a.size() - 1;
  for (long long int i = begin; i <= end; i++) {
    cout << a[i].first << " " << a[i].second << "\n";
  }
  cout << "\n";
}
void yes() { cout << "YES\n"; }
void no() { cout << "NO\n"; }
void yesno(int f) {
  if (f)
    yes();
  else
    no();
}
void solve() {
  long long int n;
  cin >> n;
  long long int p = 1;
  long long int diagjump = n + 1;
  for (long long int i = 1; i <= n; i++) {
    p = i;
    for (long long int j = 1; j <= n; j++) {
      cout << p << " ";
      if (p == n * j)
        p++;
      else
        p += diagjump;
    }
    cout << "\n";
  }
}
int main(void) {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  solve();
  return 0;
}