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 count_rem(l, r):
    tot = r-l+1
    ans = [tot//3]*3
    rem = tot % 3
    ini = l % 3
    for i in range(rem):
        ans[(ini+i) % 3] += 1
    return ans

MOD = 10**9+7

n, l, r = map(int, input().rstrip().split())
rem_table = list(map(lambda x : x%MOD, count_rem(l, r)))
dp = [[0]*3 for _ in range(n+1)]
dp[0] = [1, 0, 0]
for i in range(1, n+1):
    for j in range(3):
        for k in range(3):
            dp[i][j] = (dp[i][j] + dp[i-1][k] * rem_table[(j-k+3)%3]) % MOD
print(dp[n][0])

	     		  			   		 	 	   	