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].
from math import ceil

MOD = 10 ** 9 + 7

def f(x):
    n_max = (r - x) // 3
    n_min = int(ceil((l - x) / 3))
    return n_max - n_min + 1

n, l, r = map(int, input().split())
dp = [[0 for _ in range(3)] for _ in range(n)]

dp[0][0] = f(0)
dp[0][1] = f(1)
dp[0][2] = f(2)
for i in range(1, n):
    for j in range(3):
        for k in range(3):
            x = (3 + j - k) % 3
            y = dp[i - 1][k]
            dp[i][j] = (dp[i][j] + y * f(x)) % MOD

print(dp[n - 1][0] % MOD)
