Problem:
Score : 300 points

Problem

Takahashi, who is a novice in competitive programming, wants to learn M algorithms.
Initially, his understanding level of each of the M algorithms is 0.

Takahashi is visiting a bookstore, where he finds N books on algorithms.
The i-th book (1\leq i\leq N) is sold for C_i yen (the currency of Japan). If he buys and reads it, his understanding level of the j-th algorithm will increase by A_{i,j} for each j (1\leq j\leq M).
There is no other way to increase the understanding levels of the algorithms.

Takahashi's objective is to make his understanding levels of all the M algorithms X or higher. Determine whether this objective is achievable. If it is achievable, find the minimum amount of money needed to achieve it.

Constraints

All values in input are integers.

1\leq N, M\leq 12

1\leq X\leq 10^5

1\leq C_i \leq 10^5

0\leq A_{i, j} \leq 10^5

Input

Input is given from Standard Input in the following format:

N M X
C_1 A_{1,1} A_{1,2} \cdots A_{1,M}
C_2 A_{2,1} A_{2,2} \cdots A_{2,M}
\vdots
C_N A_{N,1} A_{N,2} \cdots A_{N,M}

Output

If the objective is not achievable, print -1; otherwise, print the minimum amount of money needed to achieve it.

Sample Input 1

3 3 10
60 2 2 4
70 8 7 9
50 2 3 9

Sample Output 1

120

Buying the second and third books makes his understanding levels of all the algorithms 10 or higher, at the minimum cost possible.

Sample Input 2

3 3 10
100 3 1 4
100 1 5 9
100 2 6 5

Sample Output 2

-1

Buying all the books is still not enough to make his understanding levels of all the algorithms 10 or higher.

Sample Input 3

8 5 22
100 3 7 5 3 1
164 4 5 2 7 8
334 7 2 7 2 9
234 4 7 2 8 2
541 5 4 3 3 6
235 4 8 6 9 7
394 3 6 1 6 2
872 8 4 3 7 2

Sample Output 3

1067

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Wrong Answer)

;;(declaim (optimize (speed 0) (safety 3) (debug 3)))
(declaim (optimize (speed 3) (safety 0) (debug 0)))

(declaim (type fixnum n m x))
(defvar n (read))
(defvar m (read))
(defvar x (read))

(defstruct book
  (price 0 :type fixnum)
  (effect (make-array m :element-type 'fixnum)
	  :type (simple-array fixnum)))

(defvar *books* (make-array n :element-type 'book))
(dotimes (i n)
  (let ((b (make-book)))
    (setf (book-price b) (read))
    (dotimes (j m)
      (setf (aref (book-effect b) j) (read)))
    (setf (aref *books* i) b)))
    
(defvar *t* (make-array (expt 2 n)
			:initial-element nil
			:element-type 'boolean))

(defun total-price (bs)
  (declare (type fixnum bs))
  (loop for b = 1 then (ash b 1)
	for bi = 0 then (1+ bi)
	while (< bi n)
	when (/= (logand b bs) 0) sum (book-price (aref *books* bi))))

(defun bit-count (i)
  (declare (type fixnum i))
  (loop for b = 1 then (ash b 1)
	while (< b (expt 2 n))
	when (/= 0 (logand b i)) sum 1))

(defun valid-combination (i)
  (declare (type fixnum i))
  (dotimes (mi m)
    (if (> x (loop for b = 1 then (ash b 1)
		for bi = 0 then (1+ bi)
		while (< b (expt 2 n))
		when (/= 0 (logand b i))
		sum (aref (book-effect (aref *books* bi)) mi)))
	(return-from valid-combination nil)))
  t)

(defun enum-next (i)
  (declare (type fixnum i))
  (loop for b = 1 then (ash b 1)
	for o = (logior b i)
	while (< b (expt 2 n))
	when (/= o i) collect o))

(defstruct (queue (:print-function print-queue))
  (front nil)
  (rear nil))

(defun print-queue (q stream depth)
  (declare (ignore depth))
  (format stream "#<Q|~s>" (queue-front q)))

(declaim (inline queue-empty))
(defun queue-empty (q)
  (declare (type queue q))
  (not (queue-front q)))

(defun queue-pop (q)
  (declare (type queue q))
  (assert (and (not (queue-empty q)) "an empty queue cannot be poped."))
  (let* ((front (queue-front q))
	 (item (car front))
	 (new-front (cdr front)))
    (declare (type cons front))
    (setf (queue-front q) new-front)
    (when (not new-front)
      (setf (queue-rear q) nil))
    item))

(defun queue-push (item q)
  (declare (type queue q))
  (let ((rear (queue-rear q))
	(new-rear (cons item nil)))
    (if rear ; if the queue is not empty
	(locally
	 (declare (type cons rear))
	 (setf (cdr rear) new-rear)
	 (setf (queue-rear q) new-rear))
      (progn
	(setf (queue-front q) new-rear)
	(setf (queue-rear q) new-rear)))))

(defvar *q* (make-queue))
(queue-push 0 *q*)

(defvar prevn -1)
(defvar ok-books nil)
(loop
 (when (queue-empty *q*)
   (return))
 (let ((item (queue-pop *q*)))
   (if (> (bit-count item) prevn)
       (if ok-books
	   (return)
	 (psetf prevn (bit-count item) ok-books nil)))
   (when (not (aref *t* item))
     (setf (aref *t* item) t)
     (dolist (next (enum-next item))
       (queue-push next *q*))
     (when (valid-combination item)
       (push item ok-books)))))

(princ (if ok-books
	   (apply #'min (mapcar #'total-price ok-books))
	 "-1"))