Score : $600$ points

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

• $0 \leq a_I,a_O,a_T,a_J,a_L,a_S,a_Z \leq 10^9$
• $a_I+a_O+a_T+a_J+a_L+a_S+a_Z \geq 1$

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.

2 1 1 0 0 0 0

3

One possible way to form the largest rectangle is shown in the following figure:

0 0 10 0 0 0 0

0

No rectangle can be formed.