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ZOJ Problem Set - 2447
November Rain

Time Limit: 5 Seconds      Memory Limit: 32768 KB

Contemporary buildings can have very complicated roofs. If we take a vertical section of such a roof it results in a number of sloping segments. When it is raining the drops are falling down on the roof straight from the sky above. Some segments are completely exposed to the rain but there may be some segments partially or even completely shielded by other segments. All the water falling onto a segment flows as a stream straight down from the lower end of the segment on the ground or possibly onto some other segment. In particular, if a stream of water is falling on an end of a segment then we consider it to be collected by this segment.

For the purpose of designing a piping system it is desired to compute how much water is flowing down from each segment of the roof. To be prepared for a heavy November rain you should count one liter of rain water falling on a meter of the horizontal plane during one second.


Write a program that:

  • reads the description of a roof,
  • computes the amount of water flowing down in one second from each segment of the roof,
  • writes the results.

Input Specification

The input consists of several test cases.
For each case, the first line contains one integer N (1 <= N <= 40 000) being the number of segments of the roof. Each of the next N lines describes one segment of the roof and contains four integers x1, y1, x2, y2 (0 <= x1, y1, x2, y2 <= 1 000 000, x1 < x2, y1 is not equal to y2) separated by single spaces. Integers x1, y1 are the horizontal position and the height of the left end of the segment respectively. Integers x2, y2 are the horizontal position and the height of the right end of the segment respectively. The segments don't have common points and there are no horizontal segments. You can also assume that there are at most 25 segments placed above any point on the ground level.

Output Specification

For each test case, print the results in N lines. The i-th line should contain the amount of water (in liters) flowing down from the i-th segment of the roof in one second.
The two consecutive cases must be separated by one blank line. But there there must be no extra blank lines at the end of the output.

Sample Input

13 7 15 6
3 8 7 7
1 7 5 6
5 5 9 3
6 3 8 2
9 6 12 8

Output for the Sample Input


Source: Central Europe 2003
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