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())
d = []
for i in range(3):
    d.append((r - i) // 3 - (l - i - 1) // 3)
mod = 10 ** 9 + 7
a, b, c = d[0], d[1], d[2]
dp = [([0] * 3) for _ in range(n)]
dp[0][0] = d[0]
dp[0][1] = d[1]
dp[0][2] = d[2]
mod = 10 ** 9 + 7
for i in range(1, n):
    x = dp[i - 1]
    dp[i][0] = (d[0] * x[0] + x[1] * d[2] + x[2] * d[1]) % mod
    dp[i][1] = (x[0] * d[1] + x[1] * d[0] + x[2] * d[2]) % mod
    dp[i][2] = (x[0] * d[2] + x[1] * d[1] + x[2] * d[0]) % mod
print(dp[n-1][0])