Ayoub had an array a of integers of size n and this array had two interesting properties: 

  * All the integers in the array were between l and r (inclusive). 
  * The sum of all the elements was divisible by 3. 



Unfortunately, Ayoub has lost his array, but he remembers the size of the array n and the numbers l and r, so he asked you to find the number of ways to restore the array. 

Since the answer could be very large, print it modulo 10^9 + 7 (i.e. the remainder when dividing by 10^9 + 7). In case there are no satisfying arrays (Ayoub has a wrong memory), print 0.

Input

The first and only line contains three integers n, l and r (1 ≤ n ≤ 2 ⋅ 10^5 , 1 ≤ l ≤ r ≤ 10^9) — the size of the lost array and the range of numbers in the array.

Output

Print the remainder when dividing by 10^9 + 7 the number of ways to restore the array.

Examples

Input


2 1 3


Output


3


Input


3 2 2


Output


1


Input


9 9 99


Output


711426616

Note

In the first example, the possible arrays are : [1,2], [2,1], [3, 3].

In the second example, the only possible array is [2, 2, 2].

import java.io.*;
import java.util.*;


public class Main {

    private static Scanner sc;
    private static Printer pr;
    private static long aLong=(long)(Math.pow(10,9)+7);
    private static long[][]dp;
    private static void solve() {
        long n=sc.nextLong();
        long l=sc.nextLong();
        long r=sc.nextLong();
        int []array1=new int[3];
        dp=new long[200006][3];
        array1[0]=(int)(r/3-(l-1)/3);
        array1[1]=(int)((r+1)/3-l/3);
        array1[2]=(int)((r+2)/3-(l+1)/3);
        dp[0][0]=1;
        for (int i=1;i<=n;i++){
            for (int j=0;j<3;j++){
                for (int k=0;k<3;k++){
                    dp[i][j]+=dp[i-1][(j+k)%3]*array1[k];
                    dp[i][j]%=aLong;
                }
            }
        }
        System.out.println(dp[(int)n][0]);

    }

    private static class Pair  {
        long a;
        long b;

        Pair(long a, long b) {
            this.a = a;
            this.b = b;
        }

        //@Override
        public int compareTo(Pair o) {
            //if (a == o.a) {
              //  return Long.compare(b, o.b);
           // }

            return Long.compare(b,o.b);
        }
    }

    public static void main(String[] args) {
        sc = new Scanner(System.in);
        pr = new Printer(System.out);

        solve();

        pr.close();
        sc.close();
    }
    private static class Scanner {
        BufferedReader br;

        Scanner (InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        private boolean isPrintable(int ch) {
            return ch >= '!' && ch <= '~';
        }

        private boolean isCRLF(int ch) {
            return ch == '\n' || ch == '\r' || ch == -1;
        }

        private int nextPrintable() {
            try {
                int ch;
                while (!isPrintable(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }

                return ch;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        String next() {
            try {
                int ch = nextPrintable();
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (isPrintable(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        int nextInt() {
            try {
                // parseInt from Integer.parseInt()
                boolean negative = false;
                int res = 0;
                int limit = -Integer.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Integer.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                int multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        long nextLong() {
            try {
                // parseLong from Long.parseLong()
                boolean negative = false;
                long res = 0;
                long limit = -Long.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Long.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                long multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        float nextFloat() {
            return Float.parseFloat(next());
        }

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

        String nextLine() {
            try {
                int ch;
                while (isCRLF(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (!isCRLF(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
//				throw new NoSuchElementException();
            }
        }
    }

    private static class Printer extends PrintWriter {
        Printer(PrintStream out) {
            super(out);
        }
    }
}