Moving Segments

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$N$ line segments (numbered $1$ through $N$) are placed on the $x$axis. For each valid $i$, the $i$th segment starts at $x = L_i$ and ends at $x = R_i$. At the time $t = 0$, all segments start moving; for each valid $i$, the $i$th segment starts moving with speed $V_i$. You need to assign a direction  left or right  to the movement of each segment, i.e. choose a sign for each $V_i$ (not necessarily the same for all segments). The resulting movement must satisfy the following condition: at the time $t = 10^{10000}$, there are no two segments that touch or intersect. Decide if it is possible to assign directions to the segments in such a way that the above condition is satisfied. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains a single integer $N$.  $N$ lines follow. For each $i$ ($1 \le i \le N$), the $i$th of these lines contains three spaceseparated integers $L_i$, $R_i$ and $V_i$. ### Output For each test case, print a single line containing the string `"YES"` if it is possible to assign the directions in a valid way or `"NO"` if it is impossible. ### Constraints  $1 \le T \le 100$  $1 \le N \le 1,000$  $1 \le L_i \lt R_i \le 10^9$ for each valid $i$  $1 \le V_i \le 10^9$ for each valid $i$  the sum of $N$ over all test cases does not exceed $2,000$ ### Example Input ``` 2 4 5 7 2 4 6 1 1 5 2 6 8 1 4 1 2 1 1 2 1 1 2 1 1 2 1 ``` ### Example Output ``` YES NO ``` ### Explanation **Example case 1:** We can assign the direction *left* to the $1$st and $2$nd segment and *right* to the $3$rd and $4$th segment. **Example case 2:** There is no valid way to assign directions to segments.Author:  wittyceaser 
Tags  wittyceaser 
Date Added:  12102019 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, SQL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS 
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