Cutting Cake
Time Limit:10000MS Memory Limit:131072K
Total Submit:413 Accepted:80
Case Time Limit:3000MS
Description Today,
Fish gives QQ a cake for her birthday. The cake is unusual, and it
looks like a square. The cake is made up of cream cells. The number of
the cells is N * N. At first every cell is connected with 4 cells that
are next to it.
Now, QQ wants to cut the cake. She has a special way to cut the
cake. Every time, she will cut a rectangle from the cake. After this
cut, the cells in the rectangle will be taken away. You know that some
cells are connected as a piece of cake. Now Fish think it's a time to
show how clever he is. As QQ's boy friend, he knows the size of the
rectangle and where QQ will cut it each time. But it's a difficult job
to calculate the number of the pieces QQ and Fish can take away after
every cut. So Fish asks your help. As Fish's best friend, can you help
the poor boy ¨C Fish?
Take the following figure for example. In the figure, the grey
cells have been taken away, while other cells are still in the cake.
After this cut, which is drawn in the red rectangle, 4 pieces of cake
will be taken away, which are the green one, the purple one, the yellow
one and the blue one.
Input The
input consists of a single test case. The first line of input contains
two positive integers N and M (1 <= N <= 1000, 1 <= M <=
10000), which are the size of cake and the numbers of cuts. The
following M lines, each contains 4 integers x1, y1, x2, y2 (1 <= x1 <= x2 <= N, 1 <= y1 <= y2 <= N), which are the coordinates of the top left cell and bottom right cell. The M rectangles are given in order.
Output The
output consists of m lines. Each line contains an integer, which is the
number of the pieces QQ and Fish may take away after this cut.
Sample Input
sample input#1
3 2
1 2 3 2
2 1 2 3
sample input#2
3 5
1 2 1 2
2 2 2 2
2 1 2 1
3 3 3 3
1 1 3 3
Sample Output
sample output#1
1
2
sample output#2
1
1
1
1
3
Source POJ Monthly--2006.06.25, Chen Xue
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