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ZOJ Problem Set - 3375
Imperishable Night

Time Limit: 2 Seconds      Memory Limit: 65536 KB

It's the eve of the Harvest Moon Festival in Gensokyo when Flandre Scarlet senses that something is wrong with the moon. It appears that the moon has been replaced by a fake moon. Someone must freeze time and find the real moon to ensure a full moon on the night of the festival. Remilia Scarlet tells her that she must go into the Bamboo Forest of the Lost (迷いの竹林) to investigate and gain enough points to remedy this.


Flandre sets off immediately. When she arrives at the entry of the Bamboo Forest of the Lost, she finds that there are n different parts. According to Remilia, there are two kinds of mysterious halidom, ITEM and TIME, that will increase Flandre's points:

  • When Flandre is at the entry, she can choose any path she hasn't choosed before and collects all ITEM and TIME there, then goes back to the entry.
  • There are two values, IV (ITEM Value) and TV (TIME Value) relating to how many points Flandre can gain when she collect a piece of ITEM or a piece of TIME.
  • The initial IV, TV and point of Flandre are all 0.
  • When she chooses a new part, her IV and TV and point keep the same as the end of he previous collection.
  • In parti, there are xi pieces of ITEM with value ai and yi pieces of TIME with value bi.
  • When she collects a piece of ITEM, her point will increase IV (point += IV), and her TV will increase ai (TV += ai) immediately as well.
  • when she collects a piece of TIME, her point will increase TV (point += TV), and her IV will increase bi (IV += bi) immediately as well.

Obviously, Flandre's IV and TV will be changing when she is collecting ITEM and TIME, thus the order of collection is important. Morever, the order of the parts she chooses is crucial too. Flandre should gain as many points as possible. Your task is to calculate the maximal point Flandre can gain.


The input contains multiple test cases (no more than 100). The first line of each case is an integer n (1 ≤ n ≤ 15), indicating the number of parts of the forest. Then follows n lines, the i-th (1 ≤ in) of them contains 4 integers ai, bi, xi, yi (0 ≤ ai, bi ≤ 20, 0 ≤ xi, yi ≤ 30), as described above.


For each case, output the maximal point Flandre can gain in a single line.

Sample Input

1 2 1 1
2 2 2 2
2 2 2 2
2 2 2 2

Sample Output





Author: LI, Dinghua
Source: ACM × Touhou
Contest: ZOJ Monthly, August 2010
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