The auditorium of Stanford University is made up of LR matrix (assume each coordinate has a chair). On the occasion of an event Chef was called as a chief guest. The auditorium was filled with males (M) and females (F), occupying one chair each. Our Chef is very curious guy, so he asks the gatekeeper some queries. The queries were as follows: Is there any KK sub-matrix in the auditorium which contains all Males or Females.

Input

The first line contains three space-separated integers L, R and Q describing the dimension of the auditorium and the number of questions Chef will ask.
Each of next L lines contains R characters (M or F).
Next Q lines contains K and a character (M or F).

Output

For each query output "yes" (without quotes) if there exist any K*K sub-matrix in the auditorium which contains all Males (if he asks about Male) or Females (if he asks about Female), otherwise output "no" (without quotes).

Constraints and Example
Input:
4 3 3
MMF
MMM
FFM
FFM
2 F
3 M
1 M

Output:
yes
no
yes

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