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.util.*;

public class C2 {
    private static void solve(int n , int l, int r) {
        int mod=(int)1e9+7;
        long[][] dp = new long[n+1][3];
        while (l%3!=0&&l<r){
            dp[1][l%3]++;
            l++;
        }
        while (r%3!=0&&l<r){
            dp[1][r%3]++;
            r--;
        }
        int val = (r-l)/3;
        dp[1][0]+=val;
        dp[1][1]+=val;
        dp[1][2]+=val;
        if (l==r||val!=0){
            dp[1][r%3]++;
        }
        for (int j = 2; j <= n; j++) {
            for (int k = 0; k < 3; k++) {
                for (int m = 0; m < 3; m++) {
                    int v = (k+m)%3;
                    dp[j][v]+=(dp[j-1][k]*dp[1][m])%mod;
                    dp[j][v]%=mod;
                }
            }
        }
        System.out.println(dp[n][0]);
    }

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
       // int tt = sc.nextInt();
        //for (int i = 0; i < tt; i++) {
            int n = sc.nextInt();
            int l = sc.nextInt();
            int r = sc.nextInt();
            solve(n,l,r);
        //}
    }

    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

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

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

        long[] readArrayLong(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }

        int[] readArrayInt(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

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

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