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 itertools import *

MOD = int(1e9 + 7)
n, l, r = tuple(map(int, input().split()))

c = list(repeat(r//3 - l//3, 3))
for i in range(r % 3, -1, -1): c[i] += 1
for i in range(0, l % 3, 1): c[i] -= 1

dp = [[0 for _ in range(3)] for _ in range(n+1)]
dp[1] = c
for i in range(2, n+1):
    dpl = dp[i-1]
    for j, k in product(range(3), repeat=2):
        dp[i][j] = (dp[i][j] + dpl[k]*c[(j+3-k)%3]) % MOD
print(dp[n][0])
