Problem Statement

A tetromino is a figure formed by joining four squares edge to edge. We will refer to the following seven kinds of tetromino as I-, O-, T-, J-, L-, S- and Z-tetrominos, respectively:

Snuke has many tetrominos. The number of I-, O-, T-, J-, L-, S- and Z-tetrominos in his possession are $a_I$, $a_O$, $a_T$, $a_J$, $a_L$, $a_S$ and $a_Z$, respectively. Snuke will join $K$ of his tetrominos to form a rectangle that is two squares tall and $2K$ squares wide. Here, the following rules must be followed:

• When placing each tetromino, rotation is allowed, but reflection is not.
• Each square in the rectangle must be covered by exactly one tetromino.
• No part of each tetromino may be outside the rectangle.

Snuke wants to form as large a rectangle as possible. Find the maximum possible value of $K$.

Constraints

• $0≤a_I,a_O,a_T,a_J,a_L,a_S,a_Z≤10^9$
• $a_I+a_O+a_T+a_J+a_L+a_S+a_Z≥1$

Input

The input is given from Standard Input in the following format:

a_I a_O a_T a_J a_L a_S a_Z

Output

Print the maximum possible value of $K$. If no rectangle can be formed, print 0.