Ruudukko

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.HashMap;
import java.util.Objects;
import java.util.StringTokenizer;

public class D430 {

	static final long mod = 1000000007;
	static final HashMap<Move, Long> cache = new HashMap<>();

	static int timesUsed = 0;
	static int timesUsedCached = 0;
	
	static int n;
	static long c = 0;
	static long[][] grid;

	public static void main(String[] args) {
		FastReader reader = new FastReader();
		PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));

		n = reader.nextInt();
		grid = new long[n][n];

		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++) {
				grid[i][j] = reader.nextLong();
			}

		reader.close();

		for (int i = 0; i < n; i++)
			for (int j = 0; j < n; j++) {
				if (grid[i][j] == 1) {
					c += 1;
					continue;
				}
				c += (sumFrom(i, j) + 1) % mod;
			}

		if (c == 0) c = 1;
		
		writer.println(c % mod);
		writer.flush();
		writer.close();
	}
	
	static long sumFrom(int y, int x) {
		timesUsed++;
		Move move = new Move(y, x);
		if (cache.containsKey(move)) {
			timesUsedCached++;
			return cache.get(move);
		}

		long value = grid[y][x];
		long sum = 0;

		if (value == 1)
			return 1;

		for (int i = 0; i < n; i++) {
			long horizontal = grid[y][i];
			long vertical = grid[i][x];

			if (horizontal < value) {
				if (horizontal == 1) {
					sum += 1;
				} else {
					sum += (sumFrom(y, i) + 1) % mod;
				}
			}
			if (vertical < value) {
				if (vertical == 1) {
					sum += 1;
				} else {
					sum += (sumFrom(i, x) + 1) % mod;
				}
			}

		}

		cache.put(move, sum);
		return sum;
	}

	static class Move {
		int y;
		int x;

		public Move(int y, int x) {
			this.y = y;
			this.x = x;
		}

		@Override
		public int hashCode() {
			return Objects.hash(x, y);
		}

		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Move other = (Move) obj;
			return x == other.x && y == other.y;
		}

		@Override
		public String toString() {
			return "Move [y=" + y + ", x=" + x + "]";
		}

	}

	static class FastReader {

		private BufferedReader br;
		private StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
				e.printStackTrace();
			}
			st = null;
			br = null;
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		String nextLine() {
			String str = "";

			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}

			return str;
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		BigInteger nextBigInteger() {
			return new BigInteger(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

	}

}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 2, 3

Verdict: ACCEPTED

Test 5

Group: 2, 3

Verdict: ACCEPTED

Test 6

Group: 2, 3

Verdict: ACCEPTED

Test 7

Group: 3

Verdict: ACCEPTED

Test 8

Group: 3

Verdict: TIME LIMIT EXCEEDED

Test 9

Group: 3

Verdict: TIME LIMIT EXCEEDED