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, LL, RR = list(map(int, input().split()))

MOD = 1000000007

R = [[0] * (N+1) for _ in range(3)]

def f(rest):

    rl = LL % 3
    rr = RR % 3

    first = LL + (rest-rl)
    if first < LL:
        first += 3
    last = RR - (rr - rest)
    if last > RR:
        last -= 3
    if first > last:
        return 0
    return  (last-first) // 3 + 1

F = [f(rest) % MOD for rest in range(3)]

for r in range(3):

    R[r][1] = F[r]


for n in range(2, N+1):
    for r in range(3):

        R[r][n] = sum([F[m] * R[(r-m)%3][n-1] for m in range(3)]) % MOD

print(R[0][N])
