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.*;

public class C_AyoubAndLostArray {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader inp = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(inp, out);
        out.close();
    }

    private static class Solver {
        private void solve(InputReader inp, PrintWriter out) {
            int n = inp.nextInt(), l = inp.nextInt(), r = inp.nextInt();
            long[] cnt = new long[3];
            long MOD = 1000000007;
            for (int i = 0; i < 3; i++) {
                int newL = l, newR = r;
                while (newL % 3 != i) newL++;
                while (newR % 3 != i && newR >= 0) newR--;
                if (newL <= newR) cnt[i] = (newR - newL) / 3 + 1;
            }

            long[][] dp = new long[n][3];
            System.arraycopy(cnt, 0, dp[0], 0, 3);

            for (int i = 1; i < n; i++) {
                for (int j = 0; j < 3; j++) {
                    for (int k = 0; k < 3; k++) {
                        dp[i][(j+k)%3] += dp[i-1][j] * cnt[k];
                    }
                }
                for (int j = 0; j < 3; j++) dp[i][j] %= MOD;
            }

            out.print(dp[n-1][0]);
        }
    }

    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}