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;
template <class T, typename A = allocator<T>>
class Vector : public vector<T, A> {
 public:
  using vector<T, A>::vector;
  Vector& operator()(size_t dummy_n) { return *this; }
};
typedef Vector<int> vi;
template <typename Int = int>
Int read() {
  Int flag = 1;
  char c = getchar();
  while ((c < '0' || c > '9') && c != '-' && c != EOF) c = getchar();
  if (c == '-') flag = -1, c = getchar();
  Int init = c & 15;
  while ((c = getchar()) >= '0' && c <= '9')
    init = (init << 3) + (init << 1) + (c & 15);
  return init * flag;
}
void read(char& a) {
  do scanf("%c", &a);
  while (isspace(a));
}
void write(const char& a) { printf("%c", a); }
char BUF[1234560];
void read(string& a) {
  scanf("%s", BUF);
  a = string(BUF);
}
void write(const string& a) { printf("%s", a.c_str()); }
inline void read(int& a) { a = read(); }
void write(const int& a) { printf("%d", a); }
void read(long long& a) { scanf("%I64d", &a); }
void write(const long long& a) { printf("%I64d", a); }
void read(double& a) { scanf("%lf", &a); }
void write(const double& a) { printf("%lf", a); }
void read(long double& a) { scanf("%Lf", &a); }
void write(const long double& a) { printf("%Lf", a); }
void read(pair<int, int>& a) { scanf("%d%d", &a.first, &a.second); }
void write(const pair<int, int>& a) { printf("%d %d", a.first, a.second); }
template <template <typename T, typename A = allocator<T>> class C, class T>
void read(C<T>& a) {
  for (auto i = a.begin(); i != a.end(); ++i) read(*i);
}
template <template <typename T, typename A = allocator<T>> class C, class T>
void write(const C<T>& a) {
  int sz = a.size();
  if (sz != 0) write(a[0]);
  for (int i = 1; i < sz; ++i) {
    write(' ');
    write(a[i]);
  }
}
template <typename T1, typename T2>
void read(T1& t1, T2& t2) {
  read(t1);
  read(t2);
}
template <typename T1, typename T2>
void write(const T1& t1, const T2& t2) {
  write(t1);
  write(' ');
  write(t2);
}
template <typename T1, typename T2, typename T3>
void read(T1& t1, T2& t2, T3& t3) {
  read(t1);
  read(t2);
  read(t3);
}
template <typename T1, typename T2, typename T3, typename T4>
void read(T1& t1, T2& t2, T3& t3, T4& t4) {
  read(t1);
  read(t2);
  read(t3);
  read(t4);
}
template <typename T1, typename T2, typename T3>
void write(const T1& t1, const T2& t2, const T3& t3) {
  write(t1);
  write(' ');
  write(t2);
  write(' ');
  write(t3);
}
template <template <typename T, typename A = allocator<T>> class C, class T>
void sort(C<T>& a) {
  sort(a.begin(), a.end());
}
template <template <typename T, typename A = allocator<T>> class C, class T>
void rsort(C<T>& a) {
  sort(a.rbegin(), a.rend());
}
template <typename T>
int sz(const T& a) {
  return int(a.size());
}
int main() {
  int n;
  read(n);
  vector<vi> fise(2);
  for (auto i = (1), j = decltype(1)(n * n); i < j; ++i, --j) {
    fise[i & 1].push_back(i);
    fise[i & 1].push_back(j);
  }
  write(fise.front()), write('\n');
  write(fise.back()), write('\n');
}