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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
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.Arrays;
import java.util.List;
import java.util.StringTokenizer;


public class Main {

	static class Task {
		
		int NN = 200005;
		int MOD = 1000000007;;
		int INF = 2000000000;
		long INFINITY = 2000000000000000000L;
		
		int [] c = new int[3];
		
		public void solve(InputReader in, PrintWriter out) {
			int n = in.nextInt(), l = in.nextInt(), r = in.nextInt();
			for(int i=0;i<3;++i)
				c[i] = f(r, i) - f(l-1, i);
			long [][] dp = new long[n + 1][3];
			for(int i=0;i<=n;++i) {
				for(int j=0;j<3;++j)
					dp[i][j] = 0;
			}
			dp[0][0] = 1;
			for(int i=1;i<=n;++i) {
				for(int j=0;j<3;++j) {
					for(int k=0;k<3;++k) {
						int jk = (j + k) % 3;
						dp[i][jk] = (dp[i][jk] + dp[i - 1][j] * c[k]) % MOD;
					}
				}
			}
			out.println(dp[n][0]);
		}
		
		int f(int num, int flag) {
			if(num == 0)
				return 0;
			int ret = num / 3;
			if(flag > 0 && num%3 >= flag) {
				++ret;
			}
			return ret;
		}
		
		class Pair {
			Integer first, second;
			public Pair() {
			}
			public Pair(int first, int second) {
				this.first = first;
				this.second = second;
			}
			@Override
			public int hashCode() {
				final int prime = 31;
				int result = 1;
				result = prime * result + getOuterType().hashCode();
				result = prime * result + first;
				result = prime * result + second;
				return result;
			}
			@Override
			public boolean equals(Object obj) {
				if (this == obj)
					return true;
				if (obj == null)
					return false;
				if (getClass() != obj.getClass())
					return false;
				Pair other = (Pair) obj;
				if (!getOuterType().equals(other.getOuterType()))
					return false;
				if (first != other.first)
					return false;
				if (second != other.second)
					return false;
				return true;
			}
			private Task getOuterType() {
				return Task.this;
			}
			
		}
		
	}
	
	static void prepareIO(boolean isFileIO) {
		//long t1 = System.currentTimeMillis();
		Task solver = new Task();
		// Standard IO
		if(!isFileIO) {
			InputStream inputStream = System.in;
	        OutputStream outputStream = System.out;
	        InputReader in = new InputReader(inputStream);
	        PrintWriter out = new PrintWriter(outputStream);
	        solver.solve(in, out);
	        //out.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        out.close();
		}
        // File IO
		else {
			String IPfilePath = System.getProperty("user.home") + "/Downloads/ip.in";
	        String OPfilePath = System.getProperty("user.home") + "/Downloads/op.out";
	        InputReader fin = new InputReader(IPfilePath);
	        PrintWriter fout = null;
	        try {
				fout = new PrintWriter(new File(OPfilePath));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
	        solver.solve(fin, fout);
	        //fout.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        fout.close();
		}
	}
	
	public static void main(String[] args) {
        prepareIO(false);
	}
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        
        public InputReader(String filePath) {
        	File file = new File(filePath);
            try {
				reader = new BufferedReader(new FileReader(file));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            tokenizer = null;
        }
        
        public String nextLine() {
        	String str = "";
        	try {
				str = reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        	return str;
        }
        
        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());
        }
        
    }

}