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 f(n,l,r):
    x = 1000000007
    num = int((r-l+1)/3)
    res = [num, num, num]
    for i in range(l+3*num, r+1):
        res[i%3] +=1
    a0 = res[0] % x
    a1 = res[1] % x
    a2 = res[2] % x
    b0 = a0
    b1 = a1
    b2 = a2
    for m in range(1, n):
        new0 = ((a0*b0)%x + (a1*b2)%x + (a2*b1)%x)%x
        new1 = ((a0*b1)%x + (a1*b0)%x + (a2*b2)%x)%x
        new2 = ((a0*b2)%x + (a1*b1)%x + (a2*b0)%x)%x
        b0 = new0
        b1 = new1
        b2 = new2
    return b0
if __name__ == '__main__':
    [n,l,r] = map(int, raw_input().rstrip().split())
    print f(n,l,r)