Randias has $$$n$$$ strings $$$s_{1}, s_{2}, \ldots, s_{n}$$$.
For two strings $$$a = \overline{a_{0} a_{1} \ldots a_{p-1}}$$$ and $$$b = \overline{b_{0} b_{1} \ldots b_{q-1}}$$$, if for all $$$i$$$ ($$$0 \le i \lt q$$$), $$$b_{i} = a_{i \bmod {p}}$$$, we say that $$$a$$$ is a period of $$$b$$$.
Now, Randias can perform the following operation:
He can perform this operation any number of times. After all the operations, he wants the following to be true: for each $$$1 \lt i \le n$$$, string $$$s_{i-1}$$$ is a period of $$$s_{i}$$$.
Help him to find the possible final strings, or determine it is impossible.
Each test contains multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) denoting the number of test cases. For each test case:
The first line contains a single integer $$$n$$$ ($$$1 \le n \le 10^5$$$).
Then follow $$$n$$$ lines. The $$$i$$$-th of these lines contains the string $$$s_{i}$$$ ($$$1 \le |s_{i}| \le 5 \cdot 10^6$$$). It is guaranteed that the strings only contain lowercase English letters.
It is guaranteed that the sum of $$$n$$$ does not exceed $$$10^5$$$, and the sum of $$$|s_{i}|$$$ does not exceed $$$5 \cdot 10^6$$$.
For each test case, if it is possible to make $$$s_{i-1}$$$ a period of $$$s_{i}$$$ for all $$$i$$$ after some operations, output "YES" (without quotes) on the first line. Then output $$$n$$$ strings in $$$n$$$ lines. The $$$i$$$-th string $$$s'_{i}$$$ represents the $$$i$$$-th string after all operations. If there are multiple answers, output any one of them.
If it is impossible to do that, output "NO" (without quotes) on the first line.
42abcabcd4bbcaacabbacabbbba3abaabbbaaaaab3abaabbbaaaaaa
NO YES abbca abbc abbcabb a YES ab aba abaabaab NO
