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

public class Main {
    private static FastReader sc = new FastReader(System.in);
    private static OutputWriter out = new OutputWriter(System.out);
    private static HashMap<Integer, Integer> graph;
    private static boolean[] partOfCycle;
    private static int[] status, leaf;
    private static boolean cycleFound;
    private static int cycleStart, n, numCycles;
    private static long M = (int) (1e9 + 7);

    public static void main(String[] args) throws Exception {
        n = sc.nextInt();
        graph = new HashMap<>();
        for (int i = 0; i < n; i++) {
            int u = sc.nextInt() - 1;
            int v = sc.nextInt() - 1;
            graph.put(u, v);
        }

        System.out.println(traverse());
    }

    private static long traverse() {
        status = new int[2 * n];        //0 means not seen, 1 means processing, 2 means visited
        leaf = new int[2 * n];
        partOfCycle = new boolean[2 * n];
        numCycles = 0;
        cycleStart = -1;
        cycleFound = false;
        HashMap<Integer, Integer> treeSize = new HashMap<>();

        for (int u : graph.keySet()) {
            if (status[u] == 0) {
                dfs(u);
            }
            if (!partOfCycle[u]) {
                if (!treeSize.containsKey(leaf[u])) {
                    treeSize.put(leaf[u], 1);
                } else {
                    treeSize.put(leaf[u], treeSize.get(leaf[u]) + 1);
                }
            }
        }
//        System.out.println(partOfCycle[81]);

        long ans = 1L;
//        System.out.println(numCycles);
        for (int u : treeSize.keySet()) {
            ans = (ans * (treeSize.get(u) + 1)) % M;
        }
//        System.out.println(treeSize);
        ans = (ans * pow(2, numCycles)) % M;
//        ans = (ans + numCycles) % M;
        return ans;
    }

    private static long pow(long a, long b) {
        long res = 1;
        while (b >= 1) {
            if (b % 2 == 1) {
                res = (res * a) % M;
            }
            a = (a * a) % M;
            b /= 2;
        }
        return res;
    }

    private static void dfs(int u) {
        status[u] = 1;
        if (!graph.containsKey(u)) {
            status[u] = 2;
            leaf[u] = u;
            return;
        }
        if (graph.get(u) == u) {
            partOfCycle[u] = true;
            leaf[u] = u;
            status[u] = 2;
            return;
        }
        if (status[graph.get(u)] == 1) {
            cycleFound = true;
            cycleStart = graph.get(u);
            numCycles++;
            partOfCycle[u] = true;
        } else if (status[graph.get(u)] == 0) {
            dfs(graph.get(u));
            if (cycleFound) {
                partOfCycle[u] = true;
                if (u == cycleStart) {
                    cycleFound = false; //close the cycle
                    cycleStart = -1;
                }
            } else {
                leaf[u] = leaf[graph.get(u)];
                partOfCycle[u] = partOfCycle[graph.get(u)];
            }
        } else if (status[graph.get(u)] == 2) {
            leaf[u] = leaf[graph.get(u)];
            partOfCycle[u] = partOfCycle[graph.get(u)];
        }
        status[u] = 2;
    }
}

class FastReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    public FastReader(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 int peek() {
        if (numChars == -1) {
            return -1;
        }
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                return -1;
            }
            if (numChars <= 0) {
                return -1;
            }
        }
        return buf[curChar];
    }

    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 == ',') {
                c = read();
            }
            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 String nextString() {
        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 isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
        StringBuilder buf = new StringBuilder();
        int c = read();
        while (c != '\n' && c != -1) {
            if (c != '\r') {
                buf.appendCodePoint(c);
            }
            c = read();
        }
        return buf.toString();
    }

    public String nextLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }

    public String nextLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines) {
            return nextLine();
        } else {
            return readLine0();
        }
    }

    public BigInteger nextBigInteger() {
        try {
            return new BigInteger(nextString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }

    public char nextCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }

    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 boolean isExhausted() {
        int value;
        while (isSpaceChar(value = peek()) && value != -1)
            read();
        return value == -1;
    }

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

    public SpaceCharFilter getFilter() {
        return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
        this.filter = filter;
    }

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

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

}