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

def get(x, resto):
    return x // 3 + (1 if x % 3 >= resto else 0)

lin = [int(i) for i in input().split()]
n = lin[0]
l = lin[1]
r = lin[2]

resto0 = get(r, 0) - get(l - 1, 0)
resto1 = get(r, 1) - get(l - 1, 1)
resto2 = get(r, 2) - get(l - 1, 2)

zero = resto0
um = resto1
dois = resto2

for i in range(1, n):
    a = (zero * resto0 + um * resto2 + dois * resto1) % MOD
    b = (zero * resto1 + um * resto0 + dois * resto2) % MOD
    c = (zero * resto2 + um * resto1 + dois * resto0) % MOD
    zero = a
    um = b
    dois = c

print(zero)

