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].
def main():
    n, l, r = map(int, raw_input().split())
    a = [(r - i) / 3 - (l - 1 - i) / 3 for i in xrange(3)]
    dp = (1, 0, 0)
    for i in xrange(n):
        dp = ((dp[0]*a[0]+dp[1]*a[2]+dp[2]*a[1]) % 1000000007, (dp[0]*a[1]+dp[1]*a[0]+dp[2]*a[2]) % 1000000007, (dp[0]*a[2]+dp[1]*a[1]+dp[2]*a[0]) % 1000000007)
    print dp[0]
main()
