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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class C {

    static long mod = 1_000_000_007;

    public static void main(String[] args) {

        MyScanner in = new MyScanner();

        int n = in.nextInt();
        int l = in.nextInt();
        int r = in.nextInt();


        int[] d = new int[3];
        d[0] = r/3 - (l-1)/3;
        d[2] = (r + 1)/3 - (l)/3;
        d[1] = (r + 2)/3 - (l + 1)/3;

        long[][] dp = new long[n + 1][3];
        dp[1][0] = d[0];
        dp[1][1] = d[1];
        dp[1][2] = d[2];

      //  System.out.println(d[0]+" "+d[1]+" "+d[2]);

        for (int i = 2; i <= n; ++i) {
            for (int j = 0; j <= 2; ++j) {
                for (int k = 0; k <= 2; ++k) {
                    dp[i][(j + k) % 3] = (dp[i][(j + k) % 3] + (dp[i-1][j] * d[k]) % mod) % mod;
                }
            }
        }

        System.out.println(dp[n][0]);

    }

    private static int cnt(String s, char c) {
        int result = 0;
        for (char ch : s.toCharArray()) {
            if (ch == c) {
                result++;
            }
        }
        return result;
    }

    // -----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

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

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    // --------------------------------------------------------

}