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 = [int(x) for x in input().split()]

mod = 10**9+7

def S(a,l,r):
    if r-l <= 10:
        s = 0
        for i in range(l,r+1):
            if i%3 == a:
                s += 1
        return s
    else:
        x,y = 0,0
        while (l+x)%3 != a:
            x += 1
        while (r+y)%3 != a:
            y -= 1
        return (r+y-a)//3 - (l+x-a)//3 + 1

T = [S(0,l,r),S(1,l,r),S(2,l,r)]


A = [T[0]]
B = [T[1]]
C = [T[2]]

for i in range(n):
    A.append(((T[0]*A[i])%mod+(B[i]*T[2])%mod+(C[i]*T[1])%mod)%mod)
    B.append(((T[0]*B[i])%mod+(T[2]*C[i])%mod+(T[1]*A[i])%mod)%mod)
    C.append(((T[0]*C[i])%mod+(T[1]*B[i])%mod+(T[2]*A[i])%mod)%mod)

print(A[-2])