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.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
import java.util.StringTokenizer;

public class Problem {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskF solver = new TaskF();
		solver.solve(1, in, out);
		out.close();
	}

	static class TaskF {

		public void solve(int testNumber, InputReader in, PrintWriter out) {
			int n = in.nextInt();
			int l = in.nextInt();
			int r = in.nextInt();

			long mod[] = new long[3];
			int x = (r - l + 1) / 3;
			int y = (r - l + 1) % 3;
			mod[0] = x;
			mod[1] = x;
			mod[2] = x;

			if (y == 1) {
				mod[l % 3]++;
			} else if (y == 2) {
				mod[l % 3]++;
				mod[r % 3]++;
			}

			long mm = 1000000007;
			long ans[] = new long[3];
			ans[0] = 1;
			ans[1] = 0;
			ans[2] = 0;
			while (n > 0) {
				if ((n & 1) == 1) {
					long t0 = (ans[0] * mod[0] + ans[1] * mod[2] + ans[2] * mod[1]) % mm;
					long t1 = (ans[0] * mod[1] + ans[1] * mod[0] + ans[2] * mod[2]) % mm;
					long t2 = (ans[0] * mod[2] + ans[2] * mod[0] + ans[1] * mod[1]) % mm;
					ans[0] = t0;
					ans[1] = t1;
					ans[2] = t2;
				}
				long x0 = (mod[0] * mod[0] + mod[1] * mod[2] + mod[2] * mod[1]) % mm;
				long x1 = (mod[0] * mod[1] + mod[1] * mod[0] + mod[2] * mod[2]) % mm;
				long x2 = (mod[0] * mod[2] + mod[2] * mod[0] + mod[1] * mod[1]) % mm;
				mod[0] = x0;
				mod[1] = x1;
				mod[2] = x2;
				n = (n >> 1);
			}
			out.println(ans[0]);
		}

	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

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

		public 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());
		}

	}
}