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].
from math import floor

if __name__ == '__main__':
    n_l_r = [int(i) for i in input().split()]
    arr = []
    module = 10 ** 9 + 7
    for i in range(3):
        arr.append(floor((n_l_r[2] - i) / 3) - floor((n_l_r[1] - i - 1) / 3))
    a = arr[0]
    b = arr[1]
    c = arr[2]
    for _ in range(1, n_l_r[0]):
        aux_arr1 = (a * arr[0] + b * arr[2] + c * arr[1]) % module
        aux_arr2 = (a * arr[1] + b * arr[0] + c * arr[2]) % module
        aux_arr3 = (a * arr[2] + b * arr[1] + c * arr[0]) % module
        a = aux_arr1
        b = aux_arr2
        c = aux_arr3
    print(a)
	 	 	 			 							   			  	 	