Problem I
Independent Inversions

Along Seabreak Path, there are $N = 3^K$ rows of flowers, with each row containing exactly $K$ flowers. In the $i$-th row ($0 \leq i \leq N - 1$), the color of the flowers is denoted by the ternary representation of $i$, with $0$ representing red, $1$ representing green, and $2$ representing blue.

E.g., if $K = 4$ and $i = 38 = 1102_{3}$. Then, the flowers in the $38$th ($0$-indexed) row are green, green, red, and blue, in that order.

Shaymin likes each row of flowers a different amount, so they assign a beauty value $B_{i}$ to each row, where $B$ is a permutation from $0$ to $N - 1$.

Two rows $i$ and $j$ are considered independent if they do not have any identical flowers in the same column.

E.g., row $i = 3 = 0010_{3}$ and row $j = 38 = 1102_{3}$ are independent, while row $i = 3 = 0010_{3}$ and row $j = 22 = 0211_{3}$ are not independent because the first flowers are both red, and the third flowers are both green.

Two rows $i$ and $j$ are considered an independent inversion if:

• $i < j$

• $B_{i} > B_{j}$

• Rows $i$ and $j$ are independent.

Help Shaymin count the number of independent inversions in Seabreak Path!

Input

The first line of the input contains two integers $N$ and $K$ ($3 \leq N \leq 177\, 147$, $1 \leq K \leq 11$), it is guaranteed $N = 3^{K}$.

The second line of the input contains $N$ integers, where the $i$-th ($0$-indexed) integer denotes $B_{i}$. It is guaranteed that $B_{i}$ is a permutation from $0$ to $N - 1$.

Output

Output a single integer denoting the number of independent inversions in Seabreak Path.

Explanation of Sample Input 1

The 2 indepedent inversions are ($0$, $4$) and ($0$, $5$). Note that while ($0$, $1$), ($0$, $2$), and ($0$, $3$) are inversions, they are not independent.

9 2
5 0 1 2 3 4 6 7 8

2