Ayoub and Lost Array

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].

inputFormat

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.

outputFormat

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].

样例

9 9 99

711426616