Prof. Slim Codeforces Solution | Codeforces Problem Solution 2022

Prof. Slim Codeforces Solution | Codeforces Problem Solution 2022

A. Prof. Slim

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

One day Prof. Slim decided to leave the kingdom of the GUC to join the kingdom of the GIU. He was given an easy online assessment to solve before joining the GIU. Citizens of the GUC were happy sad to see the prof leaving, so they decided to hack into the system and change the online assessment into a harder one so that he stays at the GUC. After a long argument, they decided to change it into the following problem.

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Given an array of 𝑛$n$ integers 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$, where 𝑎𝑖≠0$a_i\ne 0$, check if you can make this array sorted by using the following operation any number of times (possibly zero). An array is sorted if its elements are arranged in a non-decreasing order.

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1. select two indices 𝑖$i$ and 𝑗$j$ (1≤𝑖,𝑗≤𝑛$1\le i,j\le n$) such that 𝑎𝑖$a_i$ and 𝑎𝑗$a_j$ have different signs. In other words, one must be positive and one must be negative.
2. swap the signs of 𝑎𝑖$a_i$ and 𝑎𝑗$a_j$. For example if you select 𝑎𝑖=3$a_i=3$ and 𝑎𝑗=−2$a_j=-2$, then they will change to 𝑎𝑖=−3$a_i=-3$ and 𝑎𝑗=2$a_j=2$.

Prof. Slim saw that the problem is still too easy and isn't worth his time, so he decided to give it to you to solve.

Input

The first line contains a single integer 𝑡$t$ (1≤𝑡≤104$1\le t\le {10}^4$) — the number of test cases. Then 𝑡$t$ test cases follow.

The first line of each test case contains a single integer 𝑛$n$ (1≤𝑛≤105$1\le n\le {10}^5$) — the length of the array 𝑎$a$.

The next line contain 𝑛$n$ integers 𝑎1,𝑎2,…,𝑎𝑛$a_1,a_2,\dots ,a_n$ (−109≤𝑎𝑖≤109$-{10}^9\le a_i\le {10}^9$, 𝑎𝑖≠0$a_i\ne 0$) separated by spaces describing elements of the array 𝑎$a$.

It is guaranteed that the sum of 𝑛$n$ over all test cases doesn't exceed 105${10}^5$.

Output

For each test case, print "YES" if the array can be sorted in the non-decreasing order, otherwise print "NO". You can print each letter in any case (upper or lower).

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