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.util.*;
import java.io.*;
public class lostarray{
   public static long[][] table;
   public static int n;
   public static int[] poss;
   public static void main(String[] args) throws Exception {
      BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
      Scanner scan = new Scanner(System.in);
      PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
      StringTokenizer st = new StringTokenizer(bf.readLine());
      n = Integer.parseInt(st.nextToken());
      int l = Integer.parseInt(st.nextToken());
      int k = Integer.parseInt(st.nextToken());
      table = new long[n][3];
      poss = new int[3];
     poss[0] = (k-l+1)/3;
     poss[1] = (k-l+1)/3;
     poss[2] = (k-l+1)/3;
     for(int i=0; i<(k-l+1)%3; i++){
     poss[(l+i)%3]+=1;
     }
      for(int i=0; i<n; i++){
      dp(i,0);
      dp(i,1);
      dp(i,2);
      }
      out.println(table[n-1][0]%1000000007);
      out.close();
     
   }
   public static void dp(int m, int mod){
      if(n==m)
         return;
      if(m==0){
         table[m][mod] = poss[mod];
      }else{
         for(int i=0; i<3; i++){
            table[m][mod] += table[m-1][(mod-i+3)%3]*poss[i]%1000000007;
         }
      }
   }
}

