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1664. Pipeline Transportation

Time limit: 0.5 second
Memory limit: 64 MB
An oligarch Vovan, as many other oligarchs, transports oil from West Cuckooland to East Cuckooland. He owns a huge oil-producing station in West Cuckooland, an equally huge oil-refining station in East Cuckooland and a system of oil pipelines to move oil from one country to another. Vovan has a map of these pipelines on his table. He would like to know, how much oil this system can transport.
Each pipeline connects some pair of stations. All stations on the map are numbered: the producing station has number 1, the refining one has number N and the transit ones have numbers from 2 to N − 1, inclusive. Each pipeline can transport a limited quantity of oil, but in any direction. Vovan doesn't know that the Earth is round, so each station on his map has plane coordinates (xi and yi are the coordinates of i-th station). The pipelines are represented as line segments. Any pair of pipelines on the map can intersect only at endpoints. It is known, that the oil-producing station has the smallest x-coordinate of all stations, and the oil-refining station has the largest x-coordinate.


The first line contains an integer N. 2 ≤ N ≤ 10000. Next N lines contain the coordinates of the stations (xiyi) separated with a space. Coordinates are integers with absolute values no more than 108. Next line contains an integer M — the number of oil pipelines. Next M lines contain specifications of pipelines: for each pipeline, the three numbers describe a pair of stations connected by it and its flow capacity — an integer from 1 to 108. It is guaranteed that Vovan's system can transport some positive quantity of oil, and can't transport more than 2·109 oil units.


In the first line output the maximal quantity of oil that the Vovan's system can transport. In the following M lines output the transportation plan — triples of numbers (ABC), denoting that C oil units should flow from station A to station B. All pipelines should be presented exactly once in this list (even those, in which the oil flow is equal to zero). The values of C should always be non-negative.


0 0
1 1
2 0
1 2 2
2 3 1
1 2 1
2 3 1
Problem Author: Artem Melentyev
Problem Source: Ural SU Contest. Petrozavodsk Winter Session, January 2008