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].
"""
this is a standard python template for codeforces task, repo: github.com/solbiatialessandro/pyComPro/codeforces
"""
from sys import stdin as _stdin
from sys import stdout
stdin = lambda type_ = "int", sep = " ": list(map(eval(type_), _stdin.readline().split(sep)))
joint = lambda sep = " ", *args: sep.join(str(i) if type(i) != list else sep.join(map(str, i)) for i in args)
def iters(): return xrange(int(raw_input()))


def solve(n, l, r):
    l, m = l- 1, pow(10, 9) + 7
    dp = [[r/3 - l/3, (r+2)/3 - (l+2)/3, (r+1)/3 - (l+1)/3]]
    for i in range(n - 1):
        a = dp[i][0]*dp[0][0] + dp[i][2]*dp[0][1] + dp[i][1]*dp[0][2]
        b = dp[i][0]*dp[0][1] + dp[i][1]*dp[0][0] + dp[i][2]*dp[0][2]
        c = dp[i][1]*dp[0][1] + dp[i][2]*dp[0][0] + dp[i][0]*dp[0][2]
        dp.append([a%m,b%m,c%m])
    return dp[-1][0]%m

if __name__ == "__main__":
    """the solve(*args) structure is needed for testing purporses"""
    n, l, r = stdin()
    print solve(n, l, r)
