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())
l-=1
l_rems = [l//3] * 3
if l%3!=0:
	l_rems[1]+=1
if l%3==2:
	l_rems[2]+=1


r_rems = [r//3] * 3
if r%3!=0:
	r_rems[1]+=1
if r%3==2:
	r_rems[2]+=1

t = [r_rems[i] - l_rems[i] for i in range(3)]
mod = 10**9+7
a = [1, 0, 0]
for i in range(n):
	b0 = a[0] * t[0] + a[1] * t[2] + a[2] * t[1]
	b1 = a[0] * t[1] + a[1] * t[0] + a[2] * t[2]
	b2 = a[0] * t[2] + a[1] * t[1] + a[2] * t[0]
	a = [b0%mod, b1%mod, b2%mod]

print(a[0]%mod)