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].
tamanho, esquerda, direita = map(int, input().split())
aux1 = 0
aux2 = 0
aux3 = 0
inicio = esquerda
fim = direita

if((esquerda % 3) == 1):
  aux1 += 1
  aux2 += 1
  inicio = (esquerda + 2)
if((direita % 3) == 1):
  aux1 += 1
  fim = (direita - 1)
if((esquerda % 3) == 2):
  aux2 += 1
  inicio = (esquerda + 1)
if((direita % 3) == 2):
  aux1 += 1
  aux2 += 1
  fim = (direita - 2)

aux4 = ((fim - inicio) // 3)
inicio = aux1 = (aux1 + aux4)
fim = aux2 = (aux2 + aux4)
num_de_formas = aux3 = (aux3 + aux4 + 1)

for i in range(tamanho - 1):
    x = (inicio * aux3) + (fim * aux2) + (num_de_formas * aux1)
    y = (inicio * aux1) + (fim * aux3) + (num_de_formas * aux2)
    z = (inicio * aux2) + (fim * aux1) + (num_de_formas * aux3)
    
    inicio = x % 1000000007
    fim = y % 1000000007
    num_de_formas = z % 1000000007

print(num_de_formas)
	 		  			  	 	 	    		 	 			 	