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]

$1\le M\le 1000$

Subtask 2 [5/15]

$1\le M\le 50000$

Subtask 3 [8/15]

$1\le M\le 200000$

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 $x_1\ne x_2$, or $y_1\ne y_2$, or $t_1\ne t_2$.)

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.)