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].
from copy import deepcopy as dc
MOD=10 ** 9 + 7
n, l, r = map(int, input().split())
one = {}
for x in 0,1,2:
    one[x] = (r - l) // 3
last = l % 3
for i in range ((r - l) % 3 + 1):
    one[last] += 1
    last += 1
    last %= 3

res = dc(one)
for i in range(n - 1):
    zero = res[0] * one[0] + res[1] * one[2] + res[2] * one[1]
    mod_1 = res[0] * one[1] + res[1] * one[0] + res[2] * one[2]
    mod_2 = res[0] * one[2] + res[1] * one[1] + res[2] * one[0]
    res[0] = zero % MOD
    res[1] = mod_1 % MOD
    res[2] = mod_2 % MOD

print (res[0])
    