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 
{

	static StringBuilder st = new StringBuilder();
	static final int MOD = (int)1e9+7 ; 
	
	static int [][] memo ;
	static int n ; 
	static int [] rem = new int [3] ; 
	
	static int mult(long a , long b) {return (int)((1l * a * b) % MOD) ; }
	static int add(long a , long b) {return (int)((1l *a + b) % MOD) ; }
	
	
	static int dp(int idx , int r)
	{
		if(idx == n)return r == 0 ? 1 : 0 ;
		if(memo[r][idx] != -1) return memo[r][idx] ; 
		
		int ans = 0 ; 
		
		for(int i = 0 ; i < 3 ; i++)
			ans = add(ans, mult(rem[i], dp(idx + 1, (r + i) % 3)));
		
		return memo[r][idx] = ans ; 
		
	}
	
	public static void main(String[] args) throws Exception {

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		
		n = sc.nextInt();
		int l = sc.nextInt();
		int r = sc.nextInt();
		
		int divL = l - (l % 3)  + (l % 3 != 0 ? 3 : 0); 
		int divR = r - (r % 3) ; 
		
		
		Arrays.fill(rem,  (divR - divL)  / 3);
		
		for(int i = l ; i < divL ; i++)rem[i % 3]++;
		for(int i = divR ; i <= r ; i++)rem[i % 3] ++ ; 
		
		memo = new int [4][n];
		
		for(int i = 0 ; i < 4 ; i++)Arrays.fill(memo[i], -1);
		
		out.println(dp(0, 3));
		
		out.flush();
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner(InputStream in) {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() throws Exception {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

		long nextLong() throws Exception {
			return Long.parseLong(next());
		}

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

	}

	static void shuffle(int[] a) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}

}