Problem:
Score : 100 points

Problem Statement

There are N men and N women, both numbered 1, 2, \ldots, N.

For each i, j (1 \leq i, j \leq N), the compatibility of Man i and Woman j is given as an integer a_{i, j}.
If a_{i, j} = 1, Man i and Woman j are compatible; if a_{i, j} = 0, they are not.

Taro is trying to make N pairs, each consisting of a man and a woman who are compatible.
Here, each man and each woman must belong to exactly one pair.

Find the number of ways in which Taro can make N pairs, modulo 10^9 + 7.

Constraints

All values in input are integers.

1 \leq N \leq 21

a_{i, j} is 0 or 1.

Input

Input is given from Standard Input in the following format:

N
a_{1, 1} \ldots a_{1, N}
:
a_{N, 1} \ldots a_{N, N}

Output

Print the number of ways in which Taro can make N pairs, modulo 10^9 + 7.

Sample Input 1

3
0 1 1
1 0 1
1 1 1

Sample Output 1

3

There are three ways to make pairs, as follows ((i, j) denotes a pair of Man i and Woman j):

(1, 2), (2, 1), (3, 3)

(1, 2), (2, 3), (3, 1)

(1, 3), (2, 1), (3, 2)

Sample Input 2

4
0 1 0 0
0 0 0 1
1 0 0 0
0 0 1 0

Sample Output 2

1

There is one way to make pairs, as follows:

(1, 2), (2, 4), (3, 1), (4, 3)

Sample Input 3

1
0

Sample Output 3

0

Sample Input 4

21
0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 0 0 1
1 1 1 0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1 1 0
0 0 1 1 1 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1
0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 0
1 1 0 0 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0
0 1 1 0 1 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 1
0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 0 1 1 0 1 0
0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 1 1 1 1 1 1
0 0 1 0 0 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1
0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1
0 1 1 0 1 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0
0 0 1 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 0 0 1
0 1 1 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 1 1
1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 1 1 0 0 1
0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1
1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1
0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 0 1
0 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 1 1 0
1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 1 0
1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 0 0 0 0 0

Sample Output 4

102515160

Be sure to print the number modulo 10^9 + 7.

Solution in Java (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;
import java.math.*;
import java.text.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration
 
static class pair implements Comparable < pair > {
long x;
long y;
pair(long i, long j) {
    x = i;
    y = j;
}
public int compareTo(pair p) {
    if (this.x != p.x) {
        return Long.compare(this.x,p.x);
    } else {
        return Long.compare(this.y,p.y);
    }
}
public int hashCode() {
    return (x + " " + y).hashCode();
}
public String toString() {
    return x + " " + y;
}
public boolean equals(Object o) {
    pair x = (pair) o;
    return (x.x == this.x && x.y == this.y);
}
}
 
// int[] dx = {0,0,1,-1};
// int[] dy = {1,-1,0,0};
// int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
// int[] ddy = {1,-1,0,0,1,-1,-1,1};
 
int inf = (int) 1e9 + 9;
long biginf  = (long)1e18 + 7 ;
long mod =  (long)1e9+7;  
long[][] dp;
int[][] adj;
int n;
void solve() throws Exception {
    
    
        n=ni();
        dp=  new long[n][1<<n];
        for(int i=0;i<n;++i) Arrays.fill(dp[i],-1);
        adj = new int[n][n];
        for(int i=0;i<n;++i) for(int j=0;j<n;++j) adj[i][j]=ni();
        pn(recur(n-1,((1<<n) -1)));
    

}
// mask :  on mean person x we can choose , off means person x is already choosen by some id s
// s is id of tshirt
long recur(int s,int mask){
    if(s<0 & mask > 0) return 0;
    if(mask==0) return 1 ;
    if(dp[s][mask]!= -1) return dp[s][mask];
    

    

    long ans = 0;
    for(int i=0;i<n;++i){
        if(adj[s][i]==1 && ((mask&(1<<i))>0) ){
            ans = (ans + recur(s-1, mask^(1<<i)))%mod;
        }
    }
    ans = (ans + recur(s-1,mask))%mod ;

    return dp[s][mask] = ans ;
}


long pow(long a, long b) {
    long result = 1;
    while (b > 0) {
        if (b % 2 == 1) result = (result * a) % mod;
        b /= 2;
        a = (a * a) % mod;
    }
    return result;
}
 
void print(Object o) {
        System.out.println(o);
        System.out.flush();
}
long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
 
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        //System.out.println(System.currentTimeMillis() - s + "ms");
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
    }
 
 
public static void main(String[] args) throws Exception {
    new Main().run();
}
 
//output methods
private void pn(Object o) {
    out.println(o);
}
private void p(Object o) {
    out.print(o);
}
private ArrayList < ArrayList < Integer >> ng(int n, int e) {
    ArrayList < ArrayList < Integer >> g = new ArrayList < > ();
    for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());
 
    for (int i = 0; i < e; ++i) {
        int u = ni(), v = ni();
        g.get(u).add(v);
        g.get(v).add(u);
    }
 
    return g;
}
 
private ArrayList < ArrayList < pair >> nwg(int n, int e) {
    ArrayList < ArrayList < pair >> g = new ArrayList < > ();
    for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());
 
    for (int i = 0; i < e; ++i) {
        int u = ni(), v = ni(), w = ni();
        
        g.get(u).add(new pair(w, v));
        g.get(v).add(new pair(w, u));
    }
 
    return g;
}
 
 
//input methods
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
 
 
private int readByte() {
    if (lenbuf == -1) throw new InputMismatchException();
    if (ptrbuf >= lenbuf) {
        ptrbuf = 0;
        try {
            lenbuf = is.read(inbuf);
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        if (lenbuf <= 0) return -1;
    }
    return inbuf[ptrbuf++];
}
 
 
 
 
private boolean isSpaceChar(int c) {
    return !(c >= 33 && c <= 126);
}
private int skip() {
    int b;
    while ((b = readByte()) != -1 && isSpaceChar(b));
    return b;
}
 
private double nd() {
    return Double.parseDouble(ns());
}
private char nc() {
    return (char) skip();
}
 
private String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
        sb.appendCodePoint(b);
        b = readByte();
    }
    return sb.toString();
}
 
private char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while (p < n && !(isSpaceChar(b))) {
        buf[p++] = (char) b;
        b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
}
 
private char[][] nm(int n, int m) {
    char[][] map = new char[n][];
    for (int i = 0; i < n; i++) map[i] = ns(m);
    return map;
}
 
private int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++) a[i] = ni();
    return a;
}
 
private int ni() {
    int num = 0, b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private void tr(Object...o) {
    if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
}
void watch(Object...a) throws Exception {
    int i = 1;
    print("watch starts :");
    for (Object o: a) {
        //print(o);
        boolean notfound = true;
        if (o.getClass().isArray()) {
 
            String type = o.getClass().getName().toString();
            //print("type is "+type);
            switch (type) {
                case "[I":
                    {
                        int[] test = (int[]) o;
                        print(i + " " + Arrays.toString(test));
                        break;
                    }
                case "[[I":
                    {
                        int[][] obj = (int[][]) o;
 
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[J":
                    {
 
                        long[] obj = (long[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[J":
                    {
 
                        long[][] obj = (long[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[D":
                    {
 
                        double[] obj = (double[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[D":
                    {
 
                        double[][] obj = (double[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[Ljava.lang.String":
                    {
 
                        String[] obj = (String[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[Ljava.lang.String":
                    {
 
                        String[][] obj = (String[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[C":
                    {
                        char[] obj = (char[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[C":
                    {
 
                        char[][] obj = (char[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
 
 
 
                default:
                    {
                        print(i + " type not identified");
                        break;
                    }
            }
            notfound = false;
 
        }
        if (o.getClass() == ArrayList.class) {
            print(i + " al: " + o);
            notfound = false;
        }
        if (o.getClass() == HashSet.class) {
            print(i + " hs: " + o);
            notfound = false;
        }
        if (o.getClass() == TreeSet.class) {
            print(i + " ts: " + o);
            notfound = false;
        }
        if (o.getClass() == TreeMap.class) {
            print(i + " tm: " + o);
            notfound = false;
        }
        if (o.getClass() == HashMap.class) {
            print(i + " hm: " + o);
            notfound = false;
        }
        if (o.getClass() == LinkedList.class) {
            print(i + " ll: " + o);
            notfound = false;
        }
        if (o.getClass() == PriorityQueue.class) {
            print(i + " pq : " + o);
            notfound = false;
        }
        if (o.getClass() == pair.class) {
            print(i + " pq : " + o);
            notfound = false;
        }
 
        if (notfound) {
            print(i + " unknown: " + o);
        }
        i++;
    }
    print("watch ends ");
}
 
}