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 = int(1e9 + 7)
m0 = r // 3 - (l - 1) // 3
m1 = (r + 2) // 3 - (l + 1) // 3
m2 = (r + 1) // 3 - (l) // 3
a0 = 1
a1 = 0
a2 = 0
# print(m0, m1, m2)
for i in range(n):
    t0 = (a0 * m0 + a1 * m2 + a2 * m1) % mod
    t1 = (a0 * m1 + a1 * m0 + a2 * m2) % mod
    t2 = (a0 * m2 + a1 * m1 + a2 * m0) % mod
    a0, a1, a2 = t0, t1, t2
    # print(a0, a1, a2)
print(a0)