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.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class AyoubAndLostArray {
	static int n, low, high;
	static int zeros = 0, ones = 0, twos = 0;
	static int mod = (int) (1e9 + 7);
	static Long[][] dp = new Long[200006][3];

	static long go(int i, int k) {
		if (i == n)
			return k == 0 ? 1 : 0;
		if (dp[i][k] != null)
			return dp[i][k];
		long a = zeros * go(i + 1, k);
		a %= mod;
		long b = ones * go(i + 1, (k + 1) % 3);
		b %= mod;
		long c = twos * go(i + 1, (k + 2) % 3);
		c %= mod;
		return dp[i][k] = (a + b + c) % mod;
	}

	public static void main(String[] args) {
		InputReader r = new InputReader(System.in);
		n = r.nextInt();
		low = r.nextInt();
		high = r.nextInt();
		while (low <= high) {
			if (low % 3 == 0)
				break;
			if (low % 3 == 1)
				ones++;
			else if (low % 3 == 2)
				twos++;
			low++;
		}
		while (high >= low) {
			if (high % 3 == 0)
				break;
			if (high % 3 == 1)
				ones++;
			else if (high % 3 == 2)
				twos++;
			high--;
		}

		int buckets = high / 3 - low / 3;
		if (high % 3 == 0 && low % 3 == 0 && buckets >= 0) {
			zeros += buckets + 1;
			ones += buckets;
			twos += buckets;
		}
		System.out.println(go(0, 0));

	}

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

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

		public InputReader(FileReader stream) {
			reader = new BufferedReader(stream);
			tokenizer = null;
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
				return 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());
		}

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