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].
# @author Nayara Souza
# UFCG - Universidade Federal de Campina Grande
# AA - Basico

x = 10**9 + 7

n,l,r = list(map(int, input().split()))

a = r//3-(l-1)//3
b = (r+2)//3-(l+1)//3
c = (r+1)//3-(l)//3
    
y = 1
w = 0
z = 0

for i in range(n):
    k = (y*a+w*c+z*b)%x
    j = (y*b+w*a+z*c)%x
    l = (y*c+w*b+z*a)%x
    
    y,w,z = k,j,l

print(y)
  			   			 	  	   			   				