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.*;

import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
//      br = new BufferedReader(new FileReader("input.txt"));
//      PrintWriter pw = new PrintWriter("output.txt");
        int n = nextInt();
        int l = nextInt();
        int r = nextInt();
        int a[] = new int[3];
        a[0] = (int) floor((double) r / 3) - (int) ceil((double) l / 3) + 1;
        a[1] = (int) floor((double) (r - 1) / 3) - (int) ceil((double) (l - 1) / 3) + 1;
        a[2] = (int) floor((double) (r - 2) / 3) - (int) ceil((double) (l - 2) / 3) + 1;
        int dp[][] = new int[n + 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] = (int) (((long) dp[i][j] + (long) dp[i - 1][(j + k) % 3] * (long) a[k]) % mod);
        pw.println(dp[n][0] % mod);
        pw.close();
    }

    static int mod = 1_000_000_007;

    static StringTokenizer st = new StringTokenizer("");
    static BufferedReader br;

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

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

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

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