Problem:
Score : 300 points

Problem Statement

There are N+1 towns. The i-th town is being attacked by A_i monsters.

We have N heroes. The i-th hero can defeat monsters attacking the i-th or (i+1)-th town, for a total of at most B_i monsters.

What is the maximum total number of monsters the heroes can cooperate to defeat?

Constraints

All values in input are integers.

1 \leq N \leq 10^5

1 \leq A_i \leq 10^9

1 \leq B_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_{N+1}
B_1 B_2 ... B_N

Output

Print the maximum total number of monsters the heroes can defeat.

Sample Input 1

2
3 5 2
4 5

Sample Output 1

9

If the heroes choose the monsters to defeat as follows, they can defeat nine monsters in total, which is the maximum result.

The first hero defeats two monsters attacking the first town and two monsters attacking the second town.

The second hero defeats three monsters attacking the second town and two monsters attacking the third town.

Sample Input 2

3
5 6 3 8
5 100 8

Sample Output 2

22

Sample Input 3

2
100 1 1
1 100

Sample Output 3

3

Solution in Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

module ABC135

  ! <module>s to import
  use, intrinsic :: iso_fortran_env

  ! require all variables to be explicitly declared
  implicit none

  ! accessibility of <subroutine>s and <function>s in this <module>
  public :: task_C

  ! contained <subroutine>s and <function>s are below
  contains
  
  subroutine task_C

    ! variables for this <subroutine>
    integer(INT32) :: num_city
    integer(INT32) :: num_Killed_total

    ! arrays for this <subroutine>
    integer(INT64), dimension(:),   allocatable :: num_monster
    integer(INT64), dimension(:,:), allocatable :: num_Killed
    integer(INT64), dimension(:),   allocatable :: num_ToKill

    ! support variables for this <subroutine>
    integer(INT32) :: itr
    
    ! STEP.01
    ! read out the given data
    ! (length of the given sequence)
    read(unit=INPUT_UNIT, fmt=*) num_city

    ! STEP.02
    ! allocate the array to store the given data
    allocate( num_monster(1_INT32:num_city + 1_INT32) )
    allocate( num_ToKill(1_INT32:num_city) )
    allocate( num_Killed(1_INT32:2_INT32, 1_INT32:num_city) )

    ! STEP.03
    ! read out the given data
    ! (values of the given sequence)
    read(unit=INPUT_UNIT, fmt=*) num_monster(:)
    read(unit=INPUT_UNIT, fmt=*) num_ToKill(:)

    ! STEP.04
    ! calculate the answer of this task

    num_Killed(:,:)              = 0_INT64
    num_Killed(1_INT32, 1_INT32) = min( num_monster(1_INT32), num_ToKill(1_INT32) )
    num_Killed(2_INT32, 1_INT32) = min( num_monster(2_INT32), num_ToKill(1_INT32) - num_Killed(1_INT32, 1_INT32) )

    do itr = 2_INT32, num_city, 1_INT32
      num_Killed(1_INT32, itr) = min( num_monster(itr) - num_Killed(1_INT32, itr - 1_INT32), num_ToKill(itr) )
      num_Killed(2_INT32, itr) = min( num_monster(itr + 1_INT32), num_ToKill(itr) - num_Killed(1_INT32, itr) )
    end do

    num_Killed_total = 0_INT64

    do itr = 1_INT32, num_city, 1_INT32
        num_Killed_total       &!
        = num_Killed_total     &!
        + num_Killed(1_INT32, itr) &!
        + num_Killed(2_INT32, itr)
    end do

    ! STEP.05
    ! output the answer of this task
    write(unit=OUTPUT_UNIT, fmt='(I0)', advance='yes') num_Killed_total

    ! STEP.08
    ! deallocate the array to store the given data
    deallocate( num_monster        )
    deallocate( num_ToKill )
    deallocate( num_Killed )
    
    ! STEP.END
    return

  end subroutine task_C

end module ABC135

program main

  ! <module>s to import
  use, non_intrinsic :: ABC135
  
  call task_C

end program main