You are the teacher of a class of ~N~ students, all but ~M~ pairs of which are friends. A friend group is a group of ~3~ or ~4~ people such that each person in the group is friends with at least ~2~ other people in the group. Your next class assignment requires the students to work in groups of ~4~. To "encourage new friendships and social interaction," you want to see if you can pick a group of ~4~ that does not contain a friend group. Of course, friendships in the class are constantly evolving. Thus, you would like to determine whether it is still possible to pick a group of ~4~ that does not contain a friend group after each of ~Q~ changes.

Constraints

~4 \le N \le 4 \times 10^5~

~0 \le M, Q \le 4 \times 10^5~

~1 \le u_i, v_i \le N~

Subtask 1 [50%]

~4 \le N \le 5 \times 10^3~

~0 \le M, Q \le 5 \times 10^3~

Subtask 2 [50%]

No additional constraints.

Input Specification

The first line contains ~3~ integers ~N~, ~M~, and ~Q~.

The next ~M~ lines each contain ~2~ integers ~u_i~ and ~v_i~, indicating that students ~u_i~ and ~v_i~ are not friends. All pairs not mentioned here are originally friends.

The next ~Q~ lines each contain ~2~ integers ~u_i~ and ~v_i~, indicating a change in the friendship status of students ~u_i~ and ~v_i~; they become friends if they weren't friends previously and vice versa.

Output Specification

Output ~Q+1~ lines, the ~i~-th line containing the answer after the first ~i-1~ changes. The answer should be either YES if it is possible to pick a group of ~4~ that does not contain a friend group or NO otherwise.

Sample Input

6 3 1
1 2
1 3
2 4
1 2

Sample Output

YES
NO

Explanation for Sample

Initially, the graph looks like this (with edges denoting a friendship):

It can be shown that there is no friend group within the group of students ~(1, 2, 3, 4)~. However, after the update:

All groups of ~4~ contain a friend group, so it is impossible to pick a group of ~4~ that does not contain a friend group.