codeforces problem

                                     Cheap Travels (466A)

            

time limit per test:

1 secondmemory limit per test: 256 megabytes
input: standard input
    output: standard output

Ann has recently started commuting by subway. We know that a one ride subway ticket costs a rubles. Besides, Ann found out that  she can buy a special ticket for m rides (she can buy it several times). It costs b rubles. Ann did the math;  she will need to use subway n times. Help Ann, tell her what is the minimum sum of money she will have to spend to make n rides ?

Input

The single line contains  four space-separated integers n, m, a, b (1 ≤ n, m, a, b ≤ 1000) — the number of rides Ann has planned, the number of rides covered by the m ride ticket, the price of a one ride ticket and the price of an m ride ticket.

Output

Print a single integer — the minimum sum in rubles that Ann will need to spend

Examples

input

Copy

 6 2 1 2

output

Copy

 6

input

Copy

 5 2 2 3

output

Copy

 8

Note

In the first sample  one of the  optimal solutions is: each time buy a one ride ticket. There are other optimal solutions. For example, buy three m ride tickets.

                                    Holiday Of Equality(758A)

            

time limit per test:

1 second

               memory limit per test: 256 megabytes

input: standard input
output: standard output

In Berland it is the holiday of equality. In honor of the holiday the king decided to equalize the welfare of all citizens in Berland by the expense of the state treasury.

Totally in Berland there are n citizens, the welfare of each of them is estimated as the integer in ai burles (burle is the currency in Berland).

You are the royal treasurer, which needs to count the minimum charges of the kingdom on the king's present. The king can only give money, he hasn't a power to take away them.

Input

The first line contains the integer n (1 ≤ n ≤ 100) — the number of citizens in the kingdom.

The second line contains n integers a1 , a2, ..., an, where ai (0 ≤ ai ≤ 106) — the welfare of the i-th citizen.

Output

In the only line print the integer S — the minimum number of burles which are had to spend.

Examples

input

Copy

5
0 1 2 3 4

output

Copy

10

input

Copy

5
1 1 0 1 1

output

Copy

1

input

Copy

3
1 3 1

output

Copy

4

input

Copy

1
12

output

Copy

0

Note

In the first example if we add to the first citizen 4 burles, to the second 3, to the third 2 and to the fourth 1, then the welfare of all citizens will equal 4.

In the second example it is enough to give one burle to the third citizen.

In the third example it is necessary to give two burles to the first and the third citizens to make the welfare of citizens equal 3.

In the fourth example it is possible to give nothing to everyone because all citizens have 12 burles.

codeforces problems

1) codeforces problem (combination lock 540A)

time limit per test: 2 sec
memory limit per test: 256 megabytes
input: standard input
output: standard output

Scrooge McDuck keeps his most treasured savings in a home safe with a combination lock. Each time he wants to put there the treasures that he's earned fair and square, he has to open the lock.

The combination lock is represented by n rotating disks with digits from 0 to 9 written on them. Scrooge McDuck has to turn some disks so that the combination of digits on the disks forms a secret combination. In one move, he can rotate one disk one digit forwards or backwards. In particular, in one move he can go from digit 0 to digit 9 and vice versa. What minimum number of actions does he need for that?

Input

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of disks on the combination lock.

The second line contains a string of n digits — the original state of the disks.

The third line contains a string of n digits — Scrooge McDuck's combination that opens the lock.

Output

Print a single integer — the minimum number of moves Scrooge  McDuck needs to open the lock.

Examples 

input

Copy

5

82195

64723

Output

Copy

13

way-too-long-words-codeforces-problem (71A)

codeforces Way Too Long Words (71A) probem 

solution in python:-

n = int(input())
for i in range(n):
  s= input()
  if len(s)>10:
    print (s[0]+str(len(s)-2)+s[-1])
  else:
    print(s)