There are A red socks, B green socks and C Yellow socks in a dark room. Ashwin wants to find N pairs of matching colored socks from the dark room. Given all A, B and C are even and N ≤ (A+B+C)/2, write a program that outputs how many socks Ashwin would have to draw from the dark room in the worst case, to have exactly N pairs.

- Input Format

First line contains three space separated integers: A, B and C.

Second line contains the number of pairs Ashwin wants: N

- Output Format

Single line containing a single integer which is the count of socks needed to draw in the worst case

- Constraints

0 ≤ A,B,C ≤ 106

0 ≤ N ≤ (A + B + C)/2

- Example

Input 1:

2 4 4

1

Output 1:

4

Input 2:

2 4 4

4

Output 2:

9

Input 3:

2 4 4

5

Output 3:

10