Pattern Matching
Description
You 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.
Input
The 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.
Output
Print "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.
Samples
5 3 4
_b_d
__b_
aaaa
ab__
_bcd
abcd 4
abba 2
dbcd 5
YES
3 2 4 5 1
1 1 3
__c
cba 1
NO
2 2 2
a_
_b
ab 1
ab 2
NO
Note
The 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 $2$.