Comfortable Cows

문제

Farmer John's pasture can be regarded as a large 2D grid of square "cells" (picture a huge chessboard). Initially, the pasture is empty.

Farmer John will add $NN$ ($1\le N\le {10}^{5}1\backslash le\; N\backslash le\; 10^5$) cows to the pasture one by one. The $ii$th cow will occupy a cell $(x_i,y_i)(x\_i,y\_i)$ that is distinct from the cells occupied by all other cows ($0\le x_i,y_i\le 10000\backslash le\; x\_i,y\_i\backslash le\; 1000$).

A cow is said to be "comfortable" if it is horizontally or vertically adjacent to exactly three other cows. Farmer John is interested in counting the comfortable cows on his farm. For each $ii$ in the range $1\dots N1\; \backslash ldots\; N$, output the total number of comfortable cows after the $ii$th cow is added to the pasture.

입력

The first line contains a single integer $NN$. Each of the next $NN$ lines contains two space-separated integers, indicating the $(x,y)(x,y)$ coordinates of a cow's cell. It is guaranteed that all these cells are distinct.

출력

The $ii$th line of output should contain the total number of comfortable cows after the first $ii$ cows are added to the pasture.