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].
//package com.company;
import java.util.Scanner;

//2 3 4 5 6 7 8 9 10 11
public class Codeforces {
    private static int sport(int n, int l,int r) {
        long[][] dp = new long[n+1][3];
        while (l%3!=0&&l<r){
            dp[1][l%3]++;
            l++;
        }
        while (r%3!=0&&r>l){
            dp[1][r%3]++;
            r--;
        }
        int val = (r-l)/3;
            dp[1][1]+=val;
            dp[1][2]+=val;
            dp[1][0]+=val;
            if (val!=0||(r==l)) {
                dp[1][r%3]++;
            }
        int mod = (int)1e9+7;
        for (int i = 2; i < n + 1; i++) {
            for (int j = 0; j < 3; j++) {
                for (int k = 0; k < 3; k++) {
                    dp[i][(j+k)%3] += dp[i - 1][j] * dp[1][k];
                    dp[i][(j+k)%3]%=mod;
                }
            }
        }
        return (int)dp[n][0];
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int  l =sc.nextInt();
        int  r =sc.nextInt();
        System.out.println(sport(n,l,r));
    }
}