Problem: In order to do some research, n^2 labs are built on different heights of a mountain. Let's enumerate them with integers from 1 to n^2, such that the lab with the number 1 is at the lowest place, the lab with the number 2 is at the second-lowest place, …, the lab with the number n^2 is at the highest place.

To transport water between the labs, pipes are built between every pair of labs. A pipe can transport at most one unit of water at a time from the lab with the number u to the lab with the number v if u > v.

Now the labs need to be divided into n groups, each group should contain exactly n labs. The labs from different groups can transport water to each other. The sum of units of water that can be sent from a group A to a group B is equal to the number of pairs of labs (u, v) such that the lab with the number u is from the group A, the lab with the number v is from the group B and u > v. Let's denote this value as f(A,B) (i.e. f(A,B) is the sum of units of water that can be sent from a group A to a group B).

For example, if n=3 and there are 3 groups X, Y and Z: X = \{1, 5, 6\}, Y = \{2, 4, 9\} and Z = \{3, 7, 8\}. In this case, the values of f are equal to:

  * f(X,Y)=4 because of 5 → 2, 5 → 4, 6 → 2, 6 → 4, 
  * f(X,Z)=2 because of 5 → 3, 6 → 3, 
  * f(Y,X)=5 because of 2 → 1, 4 → 1, 9 → 1, 9 → 5, 9 → 6, 
  * f(Y,Z)=4 because of 4 → 3, 9 → 3, 9 → 7, 9 → 8, 
  * f(Z,X)=7 because of 3 → 1, 7 → 1, 7 → 5, 7 → 6, 8 → 1, 8 → 5, 8 → 6, 
  * f(Z,Y)=5 because of 3 → 2, 7 → 2, 7 → 4, 8 → 2, 8 → 4. 



Please, divide labs into n groups with size n, such that the value min f(A,B) over all possible pairs of groups A and B (A ≠ B) is maximal.

In other words, divide labs into n groups with size n, such that minimum number of the sum of units of water that can be transported from a group A to a group B for every pair of different groups A and B (A ≠ B) as big as possible.

Note, that the example above doesn't demonstrate an optimal division, but it demonstrates how to calculate the values f for some division.

If there are many optimal divisions, you can find any.

Input

The only line contains one number n (2 ≤ n ≤ 300).

Output

Output n lines:

In the i-th line print n numbers, the numbers of labs of the i-th group, in any order you want.

If there are multiple answers, that maximize the minimum number of the sum of units of water that can be transported from one group the another, you can print any.

Example

Input


3


Output


2 8 5
9 3 4
7 6 1

Note

In the first test we can divide 9 labs into groups \{2, 8, 5\}, \{9, 3, 4\}, \{7, 6, 1\}.

From the first group to the second group we can transport 4 units of water (8 → 3, 8 → 4, 5 → 3, 5 → 4).

From the first group to the third group we can transport 5 units of water (2 → 1, 8 → 7, 8 → 6, 8 → 1, 5 → 1).

From the second group to the first group we can transport 5 units of water (9 → 2, 9 → 8, 9 → 5, 3 → 2, 4 → 2).

From the second group to the third group we can transport 5 units of water (9 → 7, 9 → 6, 9 → 1, 3 → 1, 4 → 1).

From the third group to the first group we can transport 4 units of water (7 → 2, 7 → 5, 6 → 2, 6 → 5).

From the third group to the second group we can transport 4 units of water (7 → 3, 7 → 4, 6 → 3, 6 → 4).

The minimal number of the sum of units of water, that can be transported from one group to another is equal to 4. It can be proved, that it is impossible to make a better division.

Solution (in JAVA):

Solution:
import org.omg.CORBA.INTERNAL;
import org.omg.CORBA.Policy;

import java.io.*;
import java.math.*;
import java.util.*;
import java.lang.*;

public class Main implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();

            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }

                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        public int nextInt() {
            int c = read();

            while (isSpaceChar(c))
                c = read();

            int sgn = 1;

            if (c == '-') {
                sgn = -1;
                c = read();
            }

            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));

            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;

            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            }
            while (!isSpaceChar(c));

            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next() {
            return readString();
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    public static void main(String args[]) throws Exception {
        new Thread(null, new Main(), "Main", 1 << 26).start();
    }

    static long gcd(long a, long b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

    static long modPow(long a, long p, long m) {
        if (a == 1) return 1;
        long ans = 1;
        while (p > 0) {
            if (p % 2 == 1) ans = (ans * a) % m;
            a = (a * a) % m;
            p >>= 1;
        }
        return ans;
    }

    static long modInv(long a, long m) {
        return modPow(a, m - 2, m);
    }


    static class Radix {


        static int getMax(int arr[], int n) {
            int mx = arr[0];
            for (int i = 1; i < n; i++)
                if (arr[i] > mx)
                    mx = arr[i];
            return mx;
        }

        static void countSort(int arr[], int n, int exp) {
            int output[] = new int[n];
            int i;
            int count[] = new int[10];
            Arrays.fill(count, 0);

            for (i = 0; i < n; i++)
                count[(arr[i] / exp) % 10]++;

            for (i = 1; i < 10; i++)
                count[i] += count[i - 1];

            for (i = n - 1; i >= 0; i--) {
                output[count[(arr[i] / exp) % 10] - 1] = arr[i];
                count[(arr[i] / exp) % 10]--;
            }

            for (i = 0; i < n; i++)
                arr[i] = output[i];
        }

        static void radixsort(int arr[], int n) {
            int m = getMax(arr, n);

            for (int exp = 1; m / exp > 0; exp *= 10)
                countSort(arr, n, exp);
        }

    }

    class DSU {
        int par[], size[], connectedComponent;

        DSU(int n) {
            par = new int[n];
            size = new int[n];
            for (int i = 0; i < n; i++) {
                size[i] = 1;
                par[i] = i;
            }
            connectedComponent = n;
        }

        int root(int n) {
            if (n == par[n]) return n;
            return par[n] = root(par[n]);
        }

        boolean union(int u, int v) {
            return f_union(root(u), root(v));
        }

        boolean f_union(int u, int v) {
            if (u == v) return false;
            if (size[u] > size[v]) {
                size[u] += size[v];
                par[v] = u;
            } else {
                size[v] += size[u];
                par[u] = v;
            }
            connectedComponent--;
            return true;
        }

        DSU clone_DSU() {
            DSU t = new DSU(par.length);
            t.connectedComponent = connectedComponent;
            for (int i = 0; i < par.length; i++) {
                t.par[i] = par[i];
                t.size[i] = size[i];
            }
            return t;
        }
    }


    class segmentTree {
        long query(int cur, int l, int r, int start, int end, long tree[], long a[], long[] lazy) {
            if (l > end || r < start) return 0;
            if (lazy[cur] != 0) {
                tree[cur] += lazy[cur];
                if (l != r) {
                    lazy[2 * cur + 1] += lazy[cur];
                    lazy[2 * cur + 2] += lazy[cur];
                }
                lazy[cur] = 0;
            }
            if (l >= start && r <= end) return tree[cur];
            int mid = (l + r) >> 1;
            long p1 = query(2 * cur + 1, l, mid, start, end, tree, a, lazy);
            long p2 = query(2 * cur + 2, mid + 1, r, start, end, tree, a, lazy);
            return p1 + p2;
        }

        void build(int cur, int l, int r, long tree[], long a[]) {
            if (l == r) {
                tree[cur] = a[l];
                return;
            }
            int mid = (l + r) >> 1;
            build(2 * cur + 1, l, mid, tree, a);
            build(2 * cur + 2, mid + 1, r, tree, a);
            tree[cur] = tree[2 * cur + 1] + tree[2 * cur + 2];
        }

        void update(int cur, int start, int end, long val, int l, int r, long tree[], long a[], long[] lazy) {
            if (l > end || r < start) return;
            if (lazy[cur] != 0) {
                tree[cur] += (r - l + 1) * lazy[cur];
                if (l != r) {
                    lazy[2 * cur + 1] += lazy[cur];
                    lazy[2 * cur + 2] += lazy[cur];
                }
                lazy[cur] = 0;
            }
            if (l >= start && r <= end) {
                tree[cur] += (r - l + 1) * val;
                if (l != r) {
                    lazy[cur * 2 + 1] += val;
                    lazy[cur * 2 + 2] += val;
                }
                return;
            }
            int mid = (l + r) >> 1;
            update(2 * cur + 1, start, end, val, l, mid, tree, a, lazy);
            update(2 * cur + 2, start, end, val, mid + 1, r, tree, a, lazy);
            tree[cur] = tree[2 * cur + 1] + tree[2 * cur + 2];
        }
    }


    public void run() {
        InputReader sc = new InputReader(System.in);
        // Scanner sc=new Scanner(System.in);
        //  Random sc=new Random();
        PrintWriter out = new PrintWriter(System.out);

        int n=sc.nextInt();
        int ans[][]=new int[n][n];
        int a[][]=new int[n][n];

        int c=1;
        for (int i = 0; i <n ; i++) {
            if(i%2==0){
                for (int j = 0; j <n ; j++) {
                    ans[j][i]=c++;
                }
            }
            else{
                for (int j = n-1; j >=0 ; j--) {
                    ans[j][i]=c++;
                }
            }
        }

       /* for (int i = 0; i <n ; i++) {
            for (int j = 0; j <n ; j++) {
                if(i!=j){
                    int sum=0;
                    for (int k = 0; k <n ; k++) {
                        for (int l = 0; l <n ; l++) {
                            if(ans[i][k]>ans[j][l]){
                                sum++;
                            }
                        }
                    }
                    out.print(sum+" ");
                }
                else out.print(0+" ");
            }
            out.println();
        }*/

        for (int i = 0; i <n ; i++) {
            for (int j = 0; j <n ; j++) {
                out.print(ans[i][j]+" ");
            }
            out.println();
        }

        out.close();
    }



}