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].
import sys
range = xrange
input  = raw_input

MOD = 10**9+7

n,l,r = [int(x) for x in input().split()]
r += 1

numbs_rem = [0,0,0]
while (r-l)%3!=0:
    numbs_rem[l%3]+=1
    l+=1
numbs_rem = [(x + (r-l)//3)%MOD for x in numbs_rem]

DP = [1,0,0]
for i in range(n):
    DP = [sum(DP[i]*numbs_rem[(3-i+j)%3] for i in range(3))%MOD for j in range(3)]

print DP[0]%MOD
