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].

MOD = 10 ** 9 + 7


if __name__ == "__main__":
    n, l, r = map(int, input().split())
    a = [(r - l + 1) // 3] * 3
    t = r
    while t % 3 != (l - 1) % 3:
        a[t % 3] += 1
        t -= 1

    d = [None] * (n * 3)
    d[:3] = a
    for i in range(1, n):
        d[3 * i] = (d[3 * (i - 1)] * a[0] + d[3 * (i - 1) + 1] * a[2] + d[3 * (i - 1) + 2] * a[1]) % MOD
        d[3 * i + 1] = (d[3 * (i - 1)] * a[1] + d[3 * (i - 1) + 1] * a[0] + d[3 * (i - 1) + 2] * a[2]) % MOD
        d[3 * i + 2] = (d[3 * (i - 1)] * a[2] + d[3 * (i - 1) + 1] * a[1] + d[3 * (i - 1) + 2] * a[0]) % MOD

    print(d[-3])