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].


[n, l, r] = list(map(int, input().split(' ')))
mod = 10**9 + 7

qtd0 = r // 3 - (l-1) // 3
qtd1 = (r+1) // 3 - (l) // 3
qtd2 = (r+2) // 3 - (l+1) // 3

counts = [1, 0, 0]

for i in range(n):
    new_array = [0, 0, 0]
    new_array[0] += counts[0]*qtd0 % mod 
    new_array[0] += counts[1]*qtd2 % mod
    new_array[0] += counts[2]*qtd1 % mod
    new_array[1] += counts[0]*qtd1 % mod
    new_array[1] += counts[1]*qtd0 % mod
    new_array[1] += counts[2]*qtd2 % mod
    new_array[2] += counts[0]*qtd2 % mod
    new_array[2] += counts[1]*qtd1 % mod
    new_array[2] += counts[2]*qtd0 % mod
    counts = new_array

print(counts[0] % mod)

 	 	   	   					 	 	 	   	   		