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].
import math
import sys


def brute(l, r):
    mods = [0, 0, 0]

    for i in range(l, r+1):
        mods[i%3] += 1

    return mods

def act(l, r):
    mods = [0, 0, 0]

    mods[0] = r // 3 - (l - 1) // 3
    mods[1] = mods[0]
    if r % 3 == 0:
        mods[1] -= 1
    if l % 3 == 1:
        mods[1] += 1
    mods[2] = mods[0]
    if r % 3 == 0 or r % 3 == 1:
        mods[2] -= 1
    if l % 3 == 2 or l % 3 == 1:
        mods[2] += 1

    return mods

def main():

    n,l,r = [int(x) for x in input().split(' ')]

    mod_val = int(1e9 + 7)
    mods = act(l, r)

    dp = [[0, 0, 0] for i in range(n)]
    dp[0][0] = mods[0]
    dp[0][1] = mods[1]
    dp[0][2] = mods[2]

    for i in range(1, n):

        dp[i][0] = (dp[i-1][0] * mods[0]) % mod_val
        dp[i][0] += (dp[i-1][1] * mods[2]) % mod_val
        dp[i][0] += (dp[i-1][2] * mods[1]) % mod_val

        dp[i][1] = (dp[i-1][1] * mods[0]) % mod_val
        dp[i][1] += (dp[i-1][0] * mods[1]) % mod_val
        dp[i][1] += (dp[i-1][2] * mods[2]) % mod_val

        dp[i][2] = (dp[i-1][2] * mods[0]) % mod_val
        dp[i][2] += (dp[i-1][0] * mods[2]) % mod_val
        dp[i][2] += (dp[i-1][1] * mods[1]) % mod_val

        dp[i][0] %= mod_val
        dp[i][1] %= mod_val
        dp[i][2] %= mod_val

    print(dp[-1][0])

if __name__ == '__main__':
    main()

