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Tareq and Shawon were two friends of the problem setter's. Many years ago, they died in a road accident. The problem setter still misses them. He gives you the following task in memory of his friends.

You're given a tree with $n$ nodes and $n-1$ edges. Each node contains a single character(**A node can contain any of the lowercase Latin letters 'a' to 'z' or a special symbol '&'**). You've to answer if it is possible to find the string "**tareq&shawon**", without quotes, as a subsequence if you choose a path from the root node to a leaf node. If it is possible then print the path that contains the mentioned string as a subsequence. If there are multiple paths containing the above string as a subsequence, print the lexicographically smallest one. **Note that 1 is the root of the tree and you've to print the whole path from the root node to a leaf node that contains the above string as a subsequence**.

You have to answer t independent test cases.

The first line of the input contains one integer $t$($1 <= t <= 1000$) - the number of test cases. Then t test cases follow.

The first line of the test case contains one integer $n$($1 <= n <= 10^{5}$) - number of nodes in the tree.

The next $n-1$ lines contains two integers $u$($1 <= u <= n$) and $v$($1 <= v <= n$) denotes an edge between node $u$ and $v$.

The next line contains n space separated characters where $c[i]$ corresponds to the character in the $i^{th}$ node. $c[i]$ can be a lowercase Latin letter or special symbol '&'.

**It is guaranted that the sum of n over all test cases does not exceed $10^{5}$**

For each case print the case number and then print "YES" if there is a path from the root node to a leaf node that contains the mentioned string as a subsequence. In the next line print the lexicographically smallest path that contains the mentioned string as a subsequence.

Otherwise, print "NO".

Input | Output |
---|---|

1 31 1 2 2 3 3 8 8 9 9 13 13 17 17 18 18 23 2 4 4 7 7 10 10 14 14 16 16 19 19 22 22 28 28 29 29 30 30 31 2 5 5 6 6 11 11 12 12 15 15 20 20 21 21 24 24 25 25 26 26 27 t a r r r e e e q q q & & & s s s h h h a a a w o n m w o n x | Case 1: YES 1 2 4 7 10 14 16 19 22 28 29 30 31 |

**Explanation:**

There are two possible path from the root to a leaf that contains mentioned string as a subsequence.

They are 1 2 4 7 10 14 16 19 22 28 29 30 31 and 1 2 5 6 11 12 15 20 21 24 25 26 27.

But first one is lexicographically smaller.

78% Solution Ratio

dip_BRUREarliest,

prodip_bsmrstuFastest, 0.0s

dip_BRURLightest, 655 kB

YouKnowWhoShortest, 1435B

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