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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Washoum
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        inputClass in = new inputClass(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CAyoubAndLostArray solver = new CAyoubAndLostArray();
        solver.solve(1, in, out);
        out.close();
    }

    static class CAyoubAndLostArray {
        public void solve(int testNumber, inputClass sc, PrintWriter out) {
            int n = sc.nextInt();
            int l = sc.nextInt();
            int r = sc.nextInt();
            long[][] dp = new long[n][3];
            int first = (l / 3) * 3;
            int nb = (r) / 3 - (l - 1) / 3;
            dp[0][0] = nb;
            dp[0][1] = (r + 2) / 3 - (l + 1) / 3;
            dp[0][2] = (r + 1) / 3 - (l) / 3;
            for (int i = 1; i < n; i++) {
                dp[i][0] = ((dp[i - 1][0] * dp[0][0]) % 1000000007 + (dp[i - 1][1] * dp[0][2]) % 1000000007 + (dp[i - 1][2] * dp[0][1]) % 1000000007) % 1000000007;
                dp[i][1] = ((dp[i - 1][0] * dp[0][1]) % 1000000007 + (dp[i - 1][1] * dp[0][0]) % 1000000007 + (dp[i - 1][2] * dp[0][2]) % 1000000007) % 1000000007;
                dp[i][2] = ((dp[i - 1][0] * dp[0][2]) % 1000000007 + (dp[i - 1][2] * dp[0][0]) % 1000000007 + (dp[i - 1][1] * dp[0][1]) % 1000000007) % 1000000007;
            }
            out.println(dp[n - 1][0]);
        }

    }

    static class inputClass {
        BufferedReader br;
        StringTokenizer st;

        public inputClass(InputStream in) {

            br = new BufferedReader(new InputStreamReader(in));
        }

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

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

    }
}

