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].
if __name__ == '__main__':    
    
    nums = input().split()
    n = int(nums[0])
    l = int(nums[1])
    r = int(nums[2])
    
    additional = pow(r-l+1, n, 3) - 1.5
    if l%3 == 0 and r%3 == 0:
        additional = 2
    elif (r-l+1) % 3 == 0:
        additional = 0
    elif l%3 == 1 and r%3 == 2:
        additional = 2*((-1)**n)
    elif n%3 == 0:
        additional *= -4
    else:
        additional *= 2
    additional = int(additional)
    
    remainder = (pow(r-l+1, n, 10**9+7) + additional) % (10**9+7)
    if remainder % 3 == 0:
        print(remainder//3)
    elif remainder % 3 == 1:
        print((remainder + 10**9 + 7) // 3)
    elif remainder % 3 == 2:
        print((remainder + 2*(10**9 + 7)) // 3)