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].
M=10**9+7
n,l,r=map(int,raw_input().split())
f=[[0]*3 for _ in range(n+1)]
x=r//3
y=r%3
f[1][0]=x
f[1][1]=x
f[1][2]=x
if y>0:
	f[1][1]+=1
if y==2:
	f[1][2]+=1
x=(l-1)//3
y=(l-1)%3
f[1][0]-=x
f[1][1]-=x
f[1][2]-=x
if y>0:
	f[1][1]-=1
if y==2:
	f[1][2]-=1
for i in range(2,n+1):
	f[i][0]=(f[i-1][0]*f[1][0]+f[i-1][1]*f[1][2]+f[i-1][2]*f[1][1])%M
	f[i][1]=(f[i-1][0]*f[1][1]+f[i-1][1]*f[1][0]+f[i-1][2]*f[1][2])%M
	f[i][2]=(f[i-1][0]*f[1][2]+f[i-1][1]*f[1][1]+f[i-1][2]*f[1][0])%M
print f[-1][0]