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.util.Scanner;

public class C1105 {

    public static void main(String[] args) {
        long mod = 1000000007;
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int L = in.nextInt();
        int R = in.nextInt();
        long[] remainder = new long[3];
        for (int i=0; i<3; i++) {
           remainder[i] = Math.floorDiv(R-i, 3) - Math.floorDiv(L-1-i, 3);
        }
        long[][] stat = new long[N+1][3];
        stat[0][0] = 1;
        for (int n=1; n<=N; n++) {
            for (int i=0; i<3; i++) {
                for (int j=0; j<3; j++) {
                    stat[n][(i+j)%3] += remainder[i]*stat[n-1][j];
                    stat[n][(i+j)%3] %= mod;
                }
            }
        }
        System.out.println(stat[N][0]);
    }

}
