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())
pri=10**9+7
if(l%3==0):
    k1=r//3-l//3+1
else:
    k1=r//3-l//3

j=l-1
q=r-1
if(j%3==0):
    k2=q//3-j//3+1
else:
    k2=q//3-j//3
j=l-2
q=r-2
if(j%3==0):
    k3=q//3-j//3+1
else:
    k3=q//3-j//3
dp=[[0 for i in range(n+1)] for i in range(3)]
dp[0][1]=k1
dp[1][1]=k2
dp[2][1]=k3

for i in range(2,len(dp[0])):
    dp[0][i]=(dp[0][i-1]*k1)+(dp[1][i-1]*k3)+(dp[2][i-1]*k2)
    dp[1][i]=(dp[1][i-1]*k1)+(dp[2][i-1]*k3)+(dp[0][i-1])*k2
    dp[2][i]=(dp[2][i-1]*k1)+(dp[0][i-1]*k3)+(dp[1][i-1]*k2)
    dp[0][i]%=pri
    dp[1][i]%=pri
    dp[2][i]%=pri
print(dp[0][-1])
