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())
t=0,1,2
d=[(r-i)//3-(l-i-1)//3 for i in t]
N=(10**9+7)
 
a1=d[0]
a2=d[1]
a3=d[2]
for w in range(1,n) :
    tmp1=(a1*d[0]+a2*d[2]+a3*d[1])%N
    tmp2=(a1*d[1]+a3*d[2]+a2*d[0])%N
    tmp3=(a1*d[2]+a2*d[1]+a3*d[0])%N
    a1,a2,a3=tmp1,tmp2,tmp3
print(a1)