E. Pattern Matchingtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given n patterns p_1, p_2, \dots, p_n and m strings s_1, s_2, \dots, s_m. Each pattern p_i consists of k characters that are either lowercase Latin letters or wildcard characters (denoted by underscores). All patterns are pairwise distinct. Each string s_j consists of k lowercase Latin letters.A string a matches a pattern b if for each i from 1 to k either b_i is a wildcard character or b_i=a_i.You are asked to rearrange the patterns in such a way that the first pattern the j-th string matches is p[mt_j]. You are allowed to leave the order of the patterns unchanged.Can you perform such a rearrangement? If you can, then print any valid order.InputThe first line contains three integers n, m and k (1 \le n, m \le 10^5, 1 \le k \le 4) — the number of patterns, the number of strings and the length of each pattern and string.Each of the next n lines contains a pattern — k characters that are either lowercase Latin letters or underscores. All patterns are pairwise distinct.Each of the next m lines contains a string — k lowercase Latin letters, and an integer mt (1 \le mt \le n) — the index of the first pattern the corresponding string should match.OutputPrint "NO" if there is no way to rearrange the patterns in such a way that the first pattern that the j-th string matches is p[mt_j].Otherwise, print "YES" in the first line. The second line should contain n distinct integers from 1 to n — the order of the patterns. If there are multiple answers, print any of them.ExamplesInput
5 3 4
_b_d
__b_
aaaa
ab__
_bcd
abcd 4
abba 2
dbcd 5
Output
YES
3 2 4 5 1 
Input
1 1 3
__c
cba 1
Output
NO
Input
2 2 2
a_
_b
ab 1
ab 2
Output
NO
NoteThe order of patterns after the rearrangement in the first example is the following:   aaaa  __b_  ab__  _bcd  _b_d Thus, the first string matches patterns ab__, _bcd, _b_d in that order, the first of them is ab__, that is indeed p[4]. The second string matches __b_ and ab__, the first of them is __b_, that is p[2]. The last string matches _bcd and _b_d, the first of them is _bcd, that is p[5].The answer to that test is not unique, other valid orders also exist.In the second example cba doesn't match __c, thus, no valid order exists.In the third example the order (a_, _b) makes both strings match pattern 1 first and the order (_b, a_) makes both strings match pattern 2 first. Thus, there is no order that produces the result 1 and 2.
5 3 4
_b_d
__b_
aaaa
ab__
_bcd
abcd 4
abba 2
dbcd 5

YES 3 2 4 5 1  
['bitmasks', 'data structures', 'dfs and similar', 'graphs', 'hashing', 'sortings', 'strings', '*2300']