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].
def count(first, last):
    # an = a+(n-1)*d
    last -= fast
    last = last // d
    last += 1
    return last


n, l, r = list(map(int, input().split()))
rem = [1, 0, 0]
rem[0] = r//3-(l-1)//3
rem[1] = (r+2)//3-(l-1+2)//3
rem[2] = (r+1)//3-(l-1+1)//3

dp = [[0 for i in range(n)]for j in range(3)]
dp[0][0] = rem[0]
dp[1][0] = rem[1]
dp[2][0] = rem[2]
mod = 10 ** 9
mod += 7
for i in range(1, n):
    # state for rem 0
    dp[0][i] = (dp[0][i - 1] * rem[0]) % mod
    dp[0][i] = (dp[0][i] + (dp[1][i - 1] * rem[2]) % mod) % mod
    dp[0][i] = (dp[0][i] + (dp[2][i - 1] * rem[1]) % mod) % mod

    # if i >= 2:
    #     dp[0][i] += ((dp[1][i - 1] * dp[1][i - 2]) % mod * rem[1]) % mod
    #     dp[0][i] = dp[0][i] % mod

    # state for rem1
    dp[1][i] = (dp[1][i] + (dp[0][i - 1] * rem[1]) % mod) % mod
    dp[1][i] = (dp[1][i] + (dp[1][i - 1] * rem[0]) % mod) % mod
    dp[1][i] = (dp[1][i] + (dp[2][i - 1] * rem[2]) % mod) % mod

    # state for rem2
    dp[2][i] = (dp[2][i] + (dp[0][i - 1] * rem[2]) % mod) % mod
    dp[2][i] = (dp[2][i] + (dp[2][i - 1] * rem[0]) % mod) % mod
    dp[2][i] = (dp[2][i] + (dp[1][i - 1] * rem[1]) % mod) % mod
print(dp[0][-1])
