Elevator

problem

AOR Co., Ltd. is a $N$ story building. There is no basement floor. AOR Ika-chan is a squid, so she can go down the stairs, but not up.

I decided to install $M$ elevators in the building because it would be inconvenient if I couldn't climb upstairs. It takes time to install the elevator, and the $i$ th elevator will be installed the night after $D_i$ and will be mobile on all floors above the $A_i$ floor and below the $B_i$ floor.

You were asked $Q$ questions by AOR Ika-chan. The $i$ th question is, "Can I move from the $S_i$ floor to the $T_i$ floor at noon $E_i$ days later?" The only means of transportation are stairs and elevators. In addition, the time required for movement shall be negligible.

input

$N \ M \ Q$ $D_1 \ A_1 \ B_1$ $\ vdots$ $D_M \ A_M \ B_M$ $E_1 \ S_1 \ T_1$ $\ vdots$ $E_Q \ S_Q \ T_Q$

output

Print Yes or No on one line for each question. However, answer in the order in which they are asked. Also, output a line break at the end.

Example

Input

5 1 2 3 1 5 3 1 5 4 1 5

Output

No Yes

inputFormat

input

$N \ M \ Q$ $D_1 \ A_1 \ B_1$ $\ vdots$ $D_M \ A_M \ B_M$ $E_1 \ S_1 \ T_1$ $\ vdots$ $E_Q \ S_Q \ T_Q$

outputFormat

output

Print Yes or No on one line for each question. However, answer in the order in which they are asked. Also, output a line break at the end.

Example

Input

5 1 2 3 1 5 3 1 5 4 1 5

Output

No Yes

样例

5 1 2
3 1 5
3 1 5
4 1 5

No
Yes

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