#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define FAST ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define pb push_back
#define MOD 1000000007
#define sz5 100005
#define sz6 1000005
#define UP upper_bound
#define LB lower_bound
#define F first
#define S second
#define PI pair<int,int>
#define PL pair<ll,ll>
#define VI vector<int>
#define VL vector<ll>

map<string, int> mp;
string pat[sz5], str[sz5];
int idx[sz5];
VI gr[sz5];

VI topo;
bool cycle;
int vis[sz5];

void dfs(int idx){
    vis[idx]=2;

    for(auto it: gr[idx]){
        if(vis[it]==1)
            continue;
        if(vis[it]==2)
            cycle=true;
        else
            dfs(it);
    }
    
    topo.push_back(idx);
    vis[idx]=1;
}

bool build_edges(string &st, int id, int k){
    int la,lb;
    bool mk=false;
    for(la=0;la<(1<<k);la++){
        string temp=st;
        for(lb=0;lb<k;lb++){
            if(la&(1<<lb))
                temp[lb]='_';
        }
        auto it=mp.find(temp);
        if(it!=mp.end()){
            if(it->second==id)
                mk=true;
            else
                gr[id].push_back(it->second);
        }
    }
    return mk;
}

void test_case(void) {
    int n,m,k,la,lb;
    cin>>n>>m>>k;
    for(la=0;la<n;la++){
        cin>>pat[la];
        mp[pat[la]]=la+1;
    }

    bool mk=true;
    for(la=0;la<m;la++){
        cin>>str[la]>>idx[la];
        mk=min(mk, build_edges(str[la], idx[la], k));
    }

    if(!mk){
        cout<<"NO\n";
        return;
    }

    memset(vis, 0, sizeof(vis));
    for(la=1;la<=n;la++){
        if(!vis[la])
            dfs(la);
    }

    // for(la=1;la<=n;la++){
    //     cout<<la<<": ";
    //     for(auto it: gr[la])
    //         cout<<it<<' ';
    //     cout<<endl;
    // }
    // cout<<endl;

    if(cycle)
        cout<<"NO\n";
    else{
        cout<<"YES\n";
        for(la=n-1;la>=0;la--)
            cout<<topo[la]<<' ';
        cout<<endl;
    }
}

int main() {
    FAST

    #ifndef ONLINE_JUDGE
        freopen("in", "r", stdin);
        // freopen("out", "w", stdout);
    #endif

    int t=1;
    for(int i=1;i<=t;i++){
        // cout<<"Case #"<<i<<": ";
        test_case();
    }

    return 0;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

You are given n patterns p_1, p_2, ..., p_n and m strings s_1, s_2, ..., 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 ≤ n, m ≤ 10^5, 1 ≤ k ≤ 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 ≤ mt ≤ 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.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define FAST ios::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define ALL(a) a.begin(), a.end()
#define RALL(a) a.rbegin(), a.rend()
#define pb push_back
#define MOD 1000000007
#define sz5 100005
#define sz6 1000005
#define UP upper_bound
#define LB lower_bound
#define F first
#define S second
#define PI pair<int,int>
#define PL pair<ll,ll>
#define VI vector<int>
#define VL vector<ll>

map<string, int> mp;
string pat[sz5], str[sz5];
int idx[sz5];
VI gr[sz5];

VI topo;
bool cycle;
int vis[sz5];

void dfs(int idx){
    vis[idx]=2;

    for(auto it: gr[idx]){
        if(vis[it]==1)
            continue;
        if(vis[it]==2)
            cycle=true;
        else
            dfs(it);
    }
    
    topo.push_back(idx);
    vis[idx]=1;
}

bool build_edges(string &st, int id, int k){
    int la,lb;
    bool mk=false;
    for(la=0;la<(1<<k);la++){
        string temp=st;
        for(lb=0;lb<k;lb++){
            if(la&(1<<lb))
                temp[lb]='_';
        }
        auto it=mp.find(temp);
        if(it!=mp.end()){
            if(it->second==id)
                mk=true;
            else
                gr[id].push_back(it->second);
        }
    }
    return mk;
}

void test_case(void) {
    int n,m,k,la,lb;
    cin>>n>>m>>k;
    for(la=0;la<n;la++){
        cin>>pat[la];
        mp[pat[la]]=la+1;
    }

    bool mk=true;
    for(la=0;la<m;la++){
        cin>>str[la]>>idx[la];
        mk=min(mk, build_edges(str[la], idx[la], k));
    }

    if(!mk){
        cout<<"NO\n";
        return;
    }

    memset(vis, 0, sizeof(vis));
    for(la=1;la<=n;la++){
        if(!vis[la])
            dfs(la);
    }

    // for(la=1;la<=n;la++){
    //     cout<<la<<": ";
    //     for(auto it: gr[la])
    //         cout<<it<<' ';
    //     cout<<endl;
    // }
    // cout<<endl;

    if(cycle)
        cout<<"NO\n";
    else{
        cout<<"YES\n";
        for(la=n-1;la>=0;la--)
            cout<<topo[la]<<' ';
        cout<<endl;
    }
}

int main() {
    FAST

    #ifndef ONLINE_JUDGE
        freopen("in", "r", stdin);
        // freopen("out", "w", stdout);
    #endif

    int t=1;
    for(int i=1;i<=t;i++){
        // cout<<"Case #"<<i<<": ";
        test_case();
    }

    return 0;
}
```