Problem:
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≤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.

Sample Input 1

2 1 1 0 0 0 0

Sample Output 1

3

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

Sample Input 2

0 0 10 0 0 0 0

Sample Output 2

0

No rectangle can be formed.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil nil t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;;;
;;; Body
;;;

(define-condition fin () ())

(defun main ()
  (let* ((ai (read))
         (ao (read))
         (at (read))
         (aj (read))
         (al (read))
         (as (read))
         (az (read))
         (res 0))
    (declare (ignore at as az))
    (incf res (* ao 2))
    (when (or (zerop ai) (zerop aj) (zerop al))
      (incf res (* 4 (floor ai 2)))
      (incf res (* 4 (floor aj 2)))
      (incf res (* 4 (floor al 2)))
      (println (floor res 2))
      (return-from main))
    (assert (and (>= ai 1) (>= aj 1) (>= al 1)))
    (if (oddp ai)
        (progn (incf res (* 2 (- ai 1)))
               (setf ai 1))
        (progn (incf res (* 2 (- ai 2)))
               (setf ai 2)))
    (if (oddp aj)
        (progn (incf res (* 2 (- aj 1)))
               (setf aj 1))
        (progn (incf res (* 2 (- aj 2)))
               (setf aj 2)))
    (if (oddp al)
        (progn (incf res (* 2 (- al 1)))
               (setf al 1))
        (progn (incf res (* 2 (- al 2)))
               (setf al 2)))
    (cond ((and (= ai 2) (= aj 2) (= al 2))
           (incf res 12))
          ((and (= ai 2) (= aj 2) (= al 1))
           (incf res 8))
          ((and (= ai 2) (= aj 1) (= al 2))
           (incf res 8))
          ((and (= ai 2) (= aj 1) (= al 1))
           (incf res 6))
          ((and (= ai 1) (= aj 2) (= al 2))
           (incf res 8))
          ((and (= ai 1) (= aj 2) (= al 1))
           (incf res 6))
          ((and (= ai 1) (= aj 1) (= al 2))
           (incf res 6))
          ((and (= ai 1) (= aj 1) (= al 1))
           (incf res 6))
          (t (error "Huh?")))
    (println (floor res 2))))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+swank
(defun io-equal (in-string out-string &key (function #'main) (test #'equal))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if
the string output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (eql (uiop:last-char s) #\Linefeed)
                 s
                 (uiop:strcat s uiop:+lf+))))
    (funcall test
             (ensure-last-lf out-string)
             (with-output-to-string (out)
               (let ((*standard-output* out))
                 (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                   (funcall function)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    (run-program "C:/msys64/usr/bin/cat.exe" '("/dev/clipboard") :output out)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  "THING := null | string | symbol | pathname

null: run #'MAIN using the text on clipboard as input.
string: run #'MAIN using the string as input.
symbol: alias of FIVEAM:RUN!.
pathname: run #'MAIN using the text file as input."
  (let ((*standard-output* out))
    (etypecase thing
      (null
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "")))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "2 1 1 0 0 0 0
"
    "3
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "0 0 10 0 0 0 0
"
    "0
")))