Morris' Blog 我在摸索我存在的意義、生命的意義、內涵及價值。 沒有真正神手般的厲害，套用模式是大部分的情況。 沒那麼厲害的我存在的意義為何，襯托出神的存在？ 有時候不能怪別人不給我機會，我已經開始省思， 為什麼我沒有給別人機會的原因，而是全要靠別人。 有時候我認為我與眾不同，那是因為我做不到很多人能辦到的事情。 我聽不到、玩不起來、說得不夠明瞭、理解得不夠多， 我缺少的語文能力，就是一切一切無能的判定。 為此，我不曉得能做些對別人有幫助的事情。 我知道我自己是個不服輸的性格，但現在我不得不認輸。 我沒有能力，因此我必須認輸。 我到底來這世界作什麼？處處充滿不確定性， 而我總是無法出類拔萃，想當個一般人似乎也回不了頭了。 越強大的挑戰需要越強力的支持，而我的支持是什麼？ 最近嘗試與人談話，但都是失敗的結局，沒人能接受， 不需要言語，不需要溝通，一切所想都表達不出來。

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Problem D

Trees on My Island

Input: standard input

Output: standard output

I have bought an island where I want to plant trees in rows and columns. So, the trees will form a rectangular grid and each of them can be thought of having integer coordinates by taking a suitable grid point as the origin.

        Figure: A sample of my island

But, the problem is that the island itself is not rectangular. So, I have identified a simple polygonal area inside the island with vertices on the grid points and have decided to plant trees on grid points lying strictly inside the polygon.

Now, I seek your help for calculating the number of trees that can be planted on my island.

Input

The input file may contain multiple test cases. Each test case begins with a line containing an integer N (3 <= N <= 1,000) identifying the number of vertices of the polygon. The next N lines contain the vertices of the polygon either in clockwise or in anti-clockwise direction. Each of these N lines contains two integers identifying the x and y-coordinates of a vertex.  You may assume that none of the coordinates will be larger than 1,000,000 in absolute values.

A test case containing a zero for N in the first line terminates the input.

Output

For each test case in the input print a line containing the number of trees that can be planted inside the polygon.

Sample Input

Sample Output