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 math import *
n,l,r=[int(i) for i in input().split()]
k=[]
lr=10**9 +7
for i in range(3):
    k.append((r-i)//3 - (l-i-1)//3)
#print(k)
dp=(1,0,0)
for i in range(n):
    dp=((dp[0]*k[0] + dp[2]*k[1] + dp[1]*k[2])%lr,(dp[0]*k[1] + dp[1]*k[0]+ dp[2]*k[2])%lr,(dp[0]*k[2] + dp[2]*k[0]+ dp[1]*k[1])%lr)
print(dp[0])
