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].
n,l,r=map(int,input().split())
k=(r-l+1)//3
f,N=[[k],[k],[k]],(10**9+7)
for _ in range((r-l+1)%3):f[(r-_)%3][0]+=1
a,b,c=f[0][0],f[1][0],f[2][0]
for i  in range(n-1):
    x=(a*f[0][0]+b*f[2][0]+c*f[1][0])%N
    y=(a*f[1][0]+b*f[0][0]+c*f[2][0])%N
    z=(b*f[1][0]+c*f[0][0]+a*f[2][0])%N
    a,b,c=x,y,z
print(a)

