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())
length = l - r + 1
mod = int(1e9 + 7)

zero = r // 3 - (l - 1) // 3
one = (r + 2) // 3 - (l + 1) // 3
two = (r + 1) // 3 - (l) // 3


def num(n, s):
    rec = [[0 for j in range(3)] for i in range(n + 1)]
    rec[1][0] = zero
    rec[1][1] = two
    rec[1][2] = one
    for i in range(2, n + 1):
        for j in range(3):
            rec[i][j] = (zero * rec[i - 1][j % 3] + one * rec[i - 1][(j + 1) % 3] + two * rec[i - 1][(j + 2) % 3]) % mod
    return(rec[n][0])


result = num(n, 0)
print(result % mod)
