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 $$$a$$$.

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.

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.

Array Fix

Examples