Bob is composing a song for ~M~ singers to perform! The song lasts for ~N~ beats, and the ~x~-th singer is assigned a series of ~N~ notes ~a_{x, 1}, \dots, a_{x, N}~ to sing on each of the beats. Notes are represented by integer values, and the ~M~ notes sung on a single beat are all distinct.

Unfortunately, Bob needs to watch out for parallel-~K~s. A parallel-~K~ is a triple ~(x, y, t)~ such that ~a_{y, t} - a_{x, t} = a_{y, t+1} - a_{x, t+1} = K~. In other words, a parallel-~K~ is two singers ~x~ and ~y~, plus a beat ~t~, such that the notes that ~x~ and ~y~ sing form an interval of ~K~ on both beats ~t~ and ~t+1~.

Parallel-~K~s make music sound absolutely horrendous (for some reason), so please help Bob find all the parallel-~K~s in his song!

Constraints

~1 \le N \le 20~
~1 \le K \le 10^9~
~1 \le a_{ij} \le 10^9~
For a given ~j~, ~a_{1j}, \dots, a_{Mj}~ are distinct.

Subtask 1 [2/15]

~1 \le M \le 1\,000~

Subtask 2 [5/15]

~1 \le M \le 50\,000~

Subtask 3 [8/15]

~1 \le M \le 200\,000~

Input Specification

The first line contains three space-separated integers: ~M~, ~N~, and ~K~.
The next ~M~ lines each contain ~N~ space-separated integers, ~a_{i1}, \dots, a_{iN}~, the notes sung on each beat by singer ~i~.

Output Specification

The number of distinct parallel-~K~s in Bob's song. (Two parallel-~K~s ~(x_1, y_1, t_1)~ and ~(x_2, y_2, t_2)~ are distinct if ~x_1 \neq x_2~, or ~y_1 \neq y_2~, or ~t_1 \neq t_2~.)

Sample Input

5 3 5
5 6 6
10 11 11
15 16 16
105 116 118
110 111 113

Sample Output

5

Explanation for Sample Output

Singers 1 and 2 form two parallel-5s: one between beats 1 and 2, and another between beats 2 and 3. Singers 2 and 3 also form two parallel-5s. Finally, singers 5 and 4 form one parallel-5 between beats 2 and 3. In total, there are five parallel-5s: ~(1, 2, 1)~, ~(1, 2, 2)~, ~(2, 3, 1)~, ~(2, 3, 2)~, and ~(5, 4, 2)~. (Note that ~(4, 5, 2)~, ~(5, 4, 1)~, and ~(4, 5, 1)~ do not fit the definition of a parallel-5.)