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.Arrays;
import java.util.StringTokenizer;

public class AyoubLostArray {
    static class MyScanner {
        private BufferedReader br;
        private StringTokenizer st;

        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;
        }
    }

    static final long prime = (long)Math.pow(10,9) + 7;

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();

        int n, l, r;

        n = sc.nextInt();
        l = sc.nextInt();
        r = sc.nextInt();

        long[] dp = new long[3];
        long[] odp = new long[3];

        long[] divs = new long[3];

        divs[l % 3] = (r - l) / 3 + 1;
        divs[(l+1) % 3] = r > l ? (r - l - 1) / 3 + 1 : 0;
        divs[(l+2) % 3] = r - 1 > l ? (r - l - 2) / 3 + 1 : 0;


        System.arraycopy(divs, 0, odp, 0, 3);

        for (int i=1; i<n; ++i) {
            dp[0] = ((odp[0] * divs[0])%prime + (odp[1] * divs[2])%prime + (odp[2] * divs[1])%prime)%prime;
            dp[1] = ((odp[0] * divs[1])%prime + (odp[1] * divs[0])%prime + (odp[2] * divs[2])%prime)%prime;
            dp[2] = ((odp[0] * divs[2])%prime + (odp[2] * divs[0])%prime + (odp[1] * divs[1])%prime)%prime;

            System.arraycopy(dp, 0, odp, 0, 3);
        }


        System.out.println(odp[0]);
    }
}
