Jim and Pam were sitting in a Park when Pam booked a Uber ride to go back home. The app showed $5$ mins of ETA for the cab to arrive at their location so she thought of sharing a new idea with Jim to tease Dwight next day.

Pam has a magical array A of size N which satisfies $2$ conditions:

$1.$ All the Elements in A are greater than or equal to L and smaller than or equal to R$,$ i$.$e L $<=$ A$[$i$]<=$ R

$2.$ The sum of all the elements of array A is divisible by $3.$

Since the Uber driver came early pam left without sharing the actual array with Jim. So now Jim started thinking how many such magical arrays are possible.

Help Jim by finding how many such arrays are possible for given integers N$,$ L and R as input.

Since the answers may be large, return it with modulo $10^9+7$

Constraints:

$1<$ N $<=10^6$

$1<=$ L $<=$ R $<=10^9$

Sample:

Input: $213$

Output: $3$

Explanation: only $[1,2],[2,1][3,3]$ are possible with given N$,$L$,$R which satisfies both the conditions

$[$execution time limit$]1$ seconds $($c$)$

$[$memory limit$]1$ GB

$[$input$]$ integer n

The size of the array

$[$input$]$ integer I

Lower limit for each array element

$[$input$]$ integer r

Upper limit for each array element

$[$output$]$ integer