Break into digits

Problem Description

Given an array of integers $a$ of length $n$.

It is allowed to perform the following operation any number of times (including zero):
choose an element of the array that is at least $10$, remove it, and replace it with the digits it consists of, preserving the order of the digits and the position in the array.

For example, the number $45$ can be replaced with $(4, 5)$, and the number $10$ can be replaced with $(1, 0)$.

You need to determine whether it is possible to obtain an array sorted in non-decreasing order, that is, $a_1 \le a_2 \le \dots \le a_k,$ where is the current length of the array.

Input

In the first line, an integer $t$ ($1 \le t \le 1000$) is given — the number of input data sets.

For each set:

• in the first line, an integer $n$ ($2 \le n \le 10^5$) is given;
• in the second line, an array $a_1, a_2, \dots, a_n$ ().

The sum of $n$ across all tests does not exceed $10^5$.

Output

For each data set, output YES if it is possible to obtain a non-decreasing array, and NO otherwise.

The case of letters in the answer does not matter.

Scoring System

3
4
12 3 45 67
3
12 28 5
2
0 0

Yes
No
Yes