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E. Pattern Matching

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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.

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.

Examples

Input

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

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 $$$2$$$.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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