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 = map(int, input().split())
l = [(r - i) // 3 - (l - i - 1) // 3 for i in [0, 1, 2]]
N = 10**9 + 7
a, b, c = l[0], l[1], l[2]
for _ in range(1, n):
    i = (a * l[0] + b * l[2] + c * l[1]) % N
    j= (a * l[1] + b * l[0] + c * l[2]) % N
    k = (a * l[2] + b * l[1] + c * l[0]) % N
    a, b, c = i, j, k
print(a)
