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 = [int(v) for v in input().split()]

m = r - l
r = (
    m // 3 + 1,
    (m - 1) // 3 + 1,
    (m - 2) // 3 + 1,
)

rem = l % 3
if rem == 0:
    r0, r1, r2 = r
elif rem == 1:
    r1, r2, r0 = r
else:
    r2, r0, r1 = r

w0, w1, w2 = r0, r1, r2
mod = 1000000007

for _ in range(1, n):
    w0, w1, w2 = (
        (w0 * r0 + w1 * r2 + w2 * r1) % mod,
        (w0 * r1 + w1 * r0 + w2 * r2) % mod,
        (w0 * r2 + w1 * r1 + w2 * r0) % mod,
    )

print(w0)
