#P1948B. Array Fix
Array Fix
Description
You are given an integer array $a$ of length $n$.
You can perform the following operation any number of times (possibly zero): take any element of the array $a$, which is at least $10$, delete it, and instead insert the digits that element consisted of in the same position, in order they appear in that element.
For example:
- if we apply this operation to the $3$-rd element of the array $[12, 3, 45, 67]$, then the array becomes $[12, 3, 4, 5, 67]$.
- if we apply this operation to the $2$-nd element of the array $[2, 10]$, then the array becomes $[2, 1, 0]$.
Your task is to determine whether it is possible to make $a$ sorted in non-descending order using the aforementioned operation any number of times (possibly zero). In other words, you have to determine if it is possible to transform the array $a$ in such a way that $a_1 \le a_2 \le \dots \le a_k$, where $k$ is the current length of the array $a$.
The first line contains a single integer $t$ ($1 \le t \le 10^3$) — the number of test cases.
Each test case consists of two lines:
- the first line contains a single integer $n$ ($2 \le n \le 50$).
- the second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 99$).
For each test case, print YES if it is possible to make $a$ sorted in non-decreasing order using the aforementioned operation; otherwise, print NO.
You can print each letter in any case. For example, yes, Yes, YeS will all be recognized as a positive answer.
Input
The first line contains a single integer $t$ ($1 \le t \le 10^3$) — the number of test cases.
Each test case consists of two lines:
- the first line contains a single integer $n$ ($2 \le n \le 50$).
- the second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 99$).
Output
For each test case, print YES if it is possible to make $a$ sorted in non-decreasing order using the aforementioned operation; otherwise, print NO.
You can print each letter in any case. For example, yes, Yes, YeS will all be recognized as a positive answer.
3
4
12 3 45 67
3
12 28 5
2
0 0
YES
NO
YES
Note
In the first example, you can split the first element, then the array becomes $[1, 2, 3, 45, 67]$.
In the second example, there is no way to get a sorted array.
In the third example, the array is already sorted.