【codeforces 766D】Mahmoud and a Dictionary

time limit per test4 seconds

memory limit per test256 megabytes

inputstandard input

outputstandard output

Mahmoud wants to write a new dictionary that contains n words and relations between them. There are two types of relations: synonymy (i. e. the two words mean the same) and antonymy (i. e. the two words mean the opposite). From time to time he discovers a new relation between two words.

He know that if two words have a relation between them, then each of them has relations with the words that has relations with the other. For example, if like means love and love is the opposite of hate, then like is also the opposite of hate. One more example: if love is the opposite of hate and hate is the opposite of like, then love means like, and so on.

Sometimes Mahmoud discovers a wrong relation. A wrong relation is a relation that makes two words equal and opposite at the same time. For example if he knows that love means like and like is the opposite of hate, and then he figures out that hate means like, the last relation is absolutely wrong because it makes hate and like opposite and have the same meaning at the same time.

After Mahmoud figured out many relations, he was worried that some of them were wrong so that they will make other relations also wrong, so he decided to tell every relation he figured out to his coder friend Ehab and for every relation he wanted to know is it correct or wrong, basing on the previously discovered relations. If it is wrong he ignores it, and doesn’t check with following relations.

After adding all relations, Mahmoud asked Ehab about relations between some words based on the information he had given to him. Ehab is busy making a Codeforces round so he asked you for help.

Input

The first line of input contains three integers n, m and q (2 ≤ n ≤ 105, 1 ≤ m, q ≤ 105) where n is the number of words in the dictionary, m is the number of relations Mahmoud figured out and q is the number of questions Mahmoud asked after telling all relations.

The second line contains n distinct words a1, a2, …, an consisting of small English letters with length not exceeding 20, which are the words in the dictionary.

Then m lines follow, each of them contains an integer t (1 ≤ t ≤ 2) followed by two different words xi and yi which has appeared in the dictionary words. If t = 1, that means xi has a synonymy relation with yi, otherwise xi has an antonymy relation with yi.

Then q lines follow, each of them contains two different words which has appeared in the dictionary. That are the pairs of words Mahmoud wants to know the relation between basing on the relations he had discovered.

All words in input contain only lowercase English letters and their lengths don’t exceed 20 characters. In all relations and in all questions the two words are different.

Output

First, print m lines, one per each relation. If some relation is wrong (makes two words opposite and have the same meaning at the same time) you should print “NO” (without quotes) and ignore it, otherwise print “YES” (without quotes).

After that print q lines, one per each question. If the two words have the same meaning, output 1. If they are opposites, output 2. If there is no relation between them, output 3.

See the samples for better understanding.

Examples

input

3 3 4

hate love like

1 love like

2 love hate

1 hate like

love like

love hate

like hate

hate like

output

YES

YES

NO

1

2

2

2

input

8 6 5

hi welcome hello ihateyou goaway dog cat rat

1 hi welcome

1 ihateyou goaway

2 hello ihateyou

2 hi goaway

2 hi hello

1 hi hello

dog cat

dog hi

hi hello

ihateyou goaway

welcome ihateyou

output

YES

YES

YES

YES

NO

YES

3

3

1

1

2

【题目链接】:http://codeforces.com/contest/766/problem/D

【题意】



给你n个单词,m个关系(两个单词是反义词还是同义词);

然后问你所给的关系里面有没有错的(就是互相抵触了);

最后再给你q个询问,问你两个单词之间的关系是什么;

同义词输出1,反义词输出2,不确定输出3;

【题解】



带权并查集裸题;

不确定的关系的话,可以看看这两个单词有没有并在一起;

如果没有并在一起的话就是不确定的关系;

原题吧;

类似这道题;在代码的基础上改改就好了;

http://blog.csdn.net/harlow_cheng/article/details/52737486



【完整代码】

#include <bits/stdc++.h>

using namespace std;

const int MAXN = 1e5+100;

int n, m,q;
int f[MAXN], relation[MAXN];
string s[MAXN];
map <string,int> dic;

int findfather(int x)
{
    if (f[x] == x)
        return x;
    int olfa = f[x];
    f[x] = findfather(f[x]);
    relation[x] = (relation[x] + relation[olfa]) % 2;
    return f[x];
}

int main()
{
    //freopen("F:\\rush.txt", "r", stdin);
    cin >>n >> m >>q;
    for (int i = 1;i <= n;i++)
    {
        cin >> s[i];
        dic[s[i]] = i;
    }
        for (int i = 1; i <= n; i++)
            f[i] = i, relation[i] = 0;
        string s1,s2;
        for (int i = 1; i <= m; i++)
        {
            int z,x,y;
            cin >> z >> s1 >> s2;
            z--;
            x = dic[s1],y = dic[s2];
            int a = findfather(x), b = findfather(y);
            if (a != b)
            {
                f[b] = a;
                relation[b] = (z + relation[x] - relation[y])%2;
                puts("YES");
            }
            else
            {
                int temp = (relation[x] - relation[y] + 2) % 2;
                if (temp != z)
                        puts("NO");
                    else
                        puts("YES");
            }
        }
        for (int i = 1;i <= q;i++)
        {
            cin >> s1>>s2;
            int x = dic[s1],y = dic[s2];
            int r1 = findfather(x),r2 = findfather(y);
            if (r1!=r2)
                puts("3");
            else
            {
                int temp = (relation[x] - relation[y] + 2) % 2;
                printf("%d\n",temp+1);
            }
        }
    return 0;
}