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].

def howmanyinlrneedk(l,r):
	n = r-l+1
	L = [n//3]*3
	if n%3==0:
		return L
	elif n%3==1 :
		L[l%3]+=1
		return L
	else :
		L[l%3]+=1
		L[(l+1)%3]+=1
		return L

[m,l,r] = [int(k) for k in input().split()]
[a,b,c] = howmanyinlrneedk(l,r)


A=[a]
B=[c]
C=[b]	

for i in range(m-1):
	A.append((a*A[0]+b*B[0]+c*C[0])%(10**9+7))
	B.append((c*A[0]+a*B[0]+b*C[0])%(10**9+7))
	C.append((b*A[0]+c*B[0]+a*C[0])%(10**9+7))
	A.pop(0)
	B.pop(0)
	C.pop(0)



print(A[-1])
		





