Mishra loves to eat tomatoes. He likes tomatoes so much that he shares them with no one (not even, well, no one). Mishra likes to store his tomatoes safely. He puts all his tomatoes in boxes and puts all boxes in a $3D$ Cartesian space on the coordinates $(i,j,k)$ such that $1<=i<=N,1<=j<=N$ and $1<=k<=N$ So there are a total of $N^3$ boxes.

Now, adkroxx wants to steal his tomatoes. He has the following information :

• Number of tomatoes in each box is different.
• Number of tomatoes in any box $A_{ijk}$ is $1<= A_{ijk} <= N^3$
• The number of tomatoes in each row along positive x axis is strictly increasing.
• The number of tomatoes in each row along positive y axis is strictly increasing.
• The number of tomatoes in each row along positive z axis is strictly increasing. Now, before stealing the tomatoes, adkroxx defines $ADK_{i}$ as the product of all possible values of $A_{iii}$

$P(N)$ is given by :

Find $P(N)$ for $N=216$. Give the answer modulo $10^9+7$ .