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())
a,b,c,x,y=0,0,0,l,r
if l%3==1:a+=1;b+=1;x=l+2
if l%3==2:b+=1;x=l+1
if r%3==1:a+=1;y=r-1
if r%3==2:a+=1;b+=1;y=r-2
item=(y-x)//3
a,b,c=a+item,b+item,c+item+1
x,y,z=a,b,c
for _ in range(n-1):
    i=(x*c)+(y*b)+(z*a)
    j=(x*a)+(y*c)+(z*b)
    k=(x*b)+(y*a)+(z*c)
    x,y,z=i%1000000007,j%1000000007,k%1000000007
print(z)