A new set of desks just arrived, and it's about time! Things were getting quite cramped in the office. You've been put in charge of creating a new seating chart for the engineers. The desks are numbered, and you sent out a survey to the engineering team asking each engineer the number of the desk they currently sit at, and the number of the desk they would like to sit at (which may be the same as their current desk). Each engineer must either remain where they sit, or move to the desired seat they indicated in the survey. No two engineers currently sit at the same desk, nor may any two engineers sit at the same desk in the new seating arrangement.

How many seating arrangements can you create that meet the specified requirements? The answer may be very large, so compute it modulo 1000000007 = 109 + 7.

Input

Input will begin with a line containing N (1 ≤ N ≤ 100000), the number of engineers. 

N lines follow, each containing exactly two integers. The i-th line contains the number of the current desk of the i-th engineer and the number of the desk the i-th engineer wants to move to. Desks are numbered from 1 to 2·N. It is guaranteed that no two engineers sit at the same desk.

Output

Print the number of possible assignments, modulo 1000000007 = 109 + 7.

Examples

Input

4
1 5
5 2
3 7
7 3


Output

6


Input

5
1 10
2 10
3 10
4 10
5 5


Output

5

Note

These are the possible assignments for the first example: 

  * 1 5 3 7 
  * 1 2 3 7 
  * 5 2 3 7 
  * 1 5 7 3 
  * 1 2 7 3 
  * 5 2 7 3 
import java.io.*;
import java.util.*;

public class Solution {

    public static void main(String[] args) throws Exception {
        MyReader reader = new MyReader(System.in);
        MyWriter writer = new MyWriter(System.out);
        new Solution().run(reader, writer);
        writer.close();
    }

    private void run(MyReader reader, MyWriter writer) throws IOException {
        int n = reader.nextInt();
        int[] a = new int[2 * n];
        Arrays.fill(a, -1);
        for (int i = 0; i < n; i++) {
            int x = reader.nextInt() - 1;
            int y = reader.nextInt() - 1;
            if (x != y) {
                a[x] = y;
            } else {
                a[x] = -2;
            }
        }
        int c = 0;
        int[] b = new int[2 * n];
        for (int i = 0; i < 2 * n; i++) {
            if (b[i] == 0 && a[i] >= 0) {
                int q = i;
                while (a[q] >= 0 && b[q] == 0) {
                    b[q] = i + 1;
                    q = a[q];
                }
                if (a[q] >= 0 && b[q] == i + 1) {
                    c++;
                    while (a[q] >= 0) {
                        int w = a[q];
                        a[q] = -2;
                        q = w;
                    }
                }

            }
        }
        List<Integer>[] edges = new ArrayList[2 * n];
        for (int i = 0; i < 2 * n; i++) {
            edges[i] = new ArrayList<>();
        }
        for (int i = 0; i < 2 * n; i++) {
            if (a[i] >= 0) {
                edges[a[i]].add(i);
            }
        }
        List<Long> list = new ArrayList<>();
        for (int i = 0; i < 2 * n; i++) {
            if (a[i] == -1 && !edges[i].isEmpty()) {
                list.add(dfs(i, edges));
            }
        }
        long ans = 1;
        long mod = 1_000_000_007;
        for (long q : list) {
            ans *= q;
            ans %= mod;
        }
        for (int i = 0; i < c; i++) {
            ans <<= 1;
            ans %= mod;
        }
        writer.print(ans);
    }

    private long dfs(int n, List<Integer>[] edges) {
        int q = 1;
        for (int a : edges[n]) {
            q += dfs(a, edges);
        }
        return q;
    }

    static class MyReader {

        final BufferedInputStream in;
        final int bufSize = 1 << 16;
        final byte buf[] = new byte[bufSize];
        int i = bufSize;
        int k = bufSize;
        final StringBuilder str = new StringBuilder();

        MyReader(InputStream in) {
            this.in = new BufferedInputStream(in, bufSize);
        }

        int nextInt() throws IOException {
            return (int) nextLong();
        }

        int[] nextIntArray(int n) throws IOException {
            int[] m = new int[n];
            for (int i = 0; i < n; i++) {
                m[i] = nextInt();
            }
            return m;
        }

        int[][] nextIntMatrix(int n, int m) throws IOException {
            int[][] a = new int[n][0];
            for (int j = 0; j < n; j++) {
                a[j] = nextIntArray(m);
            }
            return a;
        }

        long nextLong() throws IOException {
            int c;
            long x = 0;
            boolean sign = true;
            while ((c = nextChar()) <= 32) ;
            if (c == '-') {
                sign = false;
                c = nextChar();
            }
            if (c == '+') {
                c = nextChar();
            }
            while (c >= '0') {
                x = x * 10 + (c - '0');
                c = nextChar();
            }
            return sign ? x : -x;
        }

        long[] nextLongArray(int n) throws IOException {
            long[] m = new long[n];
            for (int i = 0; i < n; i++) {
                m[i] = nextLong();
            }
            return m;
        }

        int nextChar() throws IOException {
            if (i == k) {
                k = in.read(buf, 0, bufSize);
                i = 0;
            }
            return i >= k ? -1 : buf[i++];
        }

        String nextString() throws IOException {
            int c;
            str.setLength(0);
            while ((c = nextChar()) <= 32 && c != -1) ;
            if (c == -1) {
                return null;
            }
            while (c > 32) {
                str.append((char) c);
                c = nextChar();
            }
            return str.toString();
        }

        String nextLine() throws IOException {
            int c;
            str.setLength(0);
            while ((c = nextChar()) <= 32 && c != -1) ;
            if (c == -1) {
                return null;
            }
            while (c != '\n') {
                str.append((char) c);
                c = nextChar();
            }
            return str.toString();
        }

        char[] nextCharArray() throws IOException {
            return nextString().toCharArray();
        }

        char[][] nextCharMatrix(int n) throws IOException {
            char[][] a = new char[n][0];
            for (int i = 0; i < n; i++) {
                a[i] = nextCharArray();
            }
            return a;
        }
    }

    static class MyWriter {

        final BufferedOutputStream out;
        final int bufSize = 1 << 16;
        final byte buf[] = new byte[bufSize];
        int i = 0;
        final byte c[] = new byte[30];
        static final String newLine = System.getProperty("line.separator");

        MyWriter(OutputStream out) {
            this.out = new BufferedOutputStream(out, bufSize);
        }

        void print(long x) throws IOException {
            int j = 0;
            if (i + 30 >= bufSize) {
                flush();
            }
            if (x < 0) {
                buf[i++] = (byte) ('-');
                x = -x;
            }
            while (j == 0 || x != 0) {
                c[j++] = (byte) (x % 10 + '0');
                x /= 10;
            }
            while (j-- > 0)
                buf[i++] = c[j];
        }

        void print(int[] m) throws IOException {
            for (int a : m) {
                print(a);
                print(' ');
            }
        }

        void print(long[] m) throws IOException {
            for (long a : m) {
                print(a);
                print(' ');
            }
        }

        void print(String s) throws IOException {
            for (int i = 0; i < s.length(); i++) {
                print(s.charAt(i));
            }
        }

        void print(char x) throws IOException {
            if (i == bufSize) {
                flush();
            }
            buf[i++] = (byte) x;
        }

        void print(char[] m) throws IOException {
            for (char c : m) {
                print(c);
            }
        }

        void println(String s) throws IOException {
            print(s);
            println();
        }

        void println() throws IOException {
            print(newLine);
        }

        void flush() throws IOException {
            out.write(buf, 0, i);
            out.flush();
            i = 0;
        }

        void close() throws IOException {
            flush();
            out.close();
        }
    }
}