You are given $n$ closed, integer intervals $[a_i, b_i]$ and $n$ integers $c_1, \ldots, c_n$.
Write a program that:
reads the number of intervals, their end points and integers $c_1, \ldots, c_n$ from the standard input, computes the minimal size of a set $Z$ of integers which has at least $c_i$ common elements with interval $[a_i, b_i]$, for each $i=1,2,\ldots,n$,
The input contain multiple test cases.
The first line of each input is an integer $n (1 \leq n \leq 50000)$ -- the number of intervals.
The following $n$ lines describe the intervals. The $(i+1)$-th line of the input contains three integers $a_i$, $b_i$ and $c_i$ separated by single spaces and such that $0 \leq a_i \leq b_i \leq 50000$ and $1 \leq c_i \leq b_i - a_i+1$.
The end-of-input is marked by a test case with $n=0$ and should not be processed.
For each test case output a single line containing the minimal size of set $Z$ sharing at least $c_i$ elements with interval $[a_i, b_i]$, for each $i=1,2,\ldots,n$.
5 3 7 3 8 10 3 6 8 1 1 3 1 10 11 1 0
6
Migrated from old NTUJ.
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