Problem:
Score: 300 points

Problem Statement

We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.

Constraints

c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

Sample Input 1

1 0 1
2 1 2
1 0 1

Sample Output 1

Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Sample Input 2

2 2 2
2 1 2
2 2 2

Sample Output 2

No

Takahashi is incorrect in this case.

Sample Input 3

0 8 8
0 8 8
0 8 8

Sample Output 3

Yes

Sample Input 4

1 8 6
2 9 7
0 7 7

Sample Output 4

No

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

(defun solver ()
  (let ((c1 (make-array 9 :fill-pointer 0))
        (c2 (make-array 9))
        (a (make-array 3))
        (b (make-array 3)))
    (loop repeat 9 do
          (vector-push (read) c1))
    (setf (aref a 0) 0
          (aref b 0) (aref c1 0)
          (aref b 1) (aref c1 1)
          (aref b 2) (aref c1 2)
          (aref a 1) (- (aref c1 3) (aref b 0))
          (aref a 2) (- (aref c1 6) (aref b 0)))
    (loop for i from 0 to 2 do
          (setf (aref c2 i) (+ (aref a 0) (aref b i))
                (aref c2 (+ i 3)) (+ (aref a 1) (aref b i))
                (aref c2 (+ i 6)) (+ (aref a 2) (aref b i))))
    (if (equalp c1 c2)
        (format t "Yes~%")
        (format t "No~%"))))

(solver)