Description

Farmer John wants to take Bessie skiing in Colorado. Sadly, Bessie is not really a very good skier.

Bessie has learned that the ski resort is offering S (0 <= S <= 100) ski classes throughout the day. Lesson i starts at time $M_i$ (1 <= $M_i$ <= 10,000) and lasts for time $L_i$ (1 <= $L_i$ <= 10,000). After lesson i, Bessie's ski ability becomes $A_i$ (1 <= $A_i$ <= 100). Note: this ability is an absolute, not an incremental change.

Bessie has purchased a map which shows all N (1 <= N <= 10,000) ski slopes along with the time $D_i$ (1 <= $D_i$ <= 10,000) required to ski down slope i and the skill level $C_i$ (1 <= $C_i$ <= 100) required to get down the slope safely. Bessie's skill level must be greater than or equal to the skill level of the slope in order for her to ski down it.

Bessie can devote her time to skiing, taking lessons, or sipping hot cocoa but must leave the ski resort by time T (1 <= T <= 10,000), and that means she must complete the descent of her last slope without exceeding that time limit.

Find the maximum number of runs Bessie can complete within the time limit. She starts the day at skill level 1.

Extra feedback will be provided on the first 50 submissions.

Description

Farmer John 想要带着 Bessie 一起在科罗拉多州一起滑雪。很不幸，Bessie滑雪技术并不精湛。

Bessie了解到，在滑雪场里，每天会提供S(0<=S<=100)门滑雪课。第i节课始于$M_i$(1<=$M_i$<=10000),上的时间为$L_i$(1<=$L_i$<=10000)。上完第i节课后，Bessie的滑雪能力会变成$A_i$(1<=$A_i$<=100). 注意：这个能力是绝对的，不是能力的增长值。

Bessie买了一张地图，地图上显示了N(1 <= N <= 10,000)个可供滑雪的斜坡，从第i个斜坡的顶端滑至底部所需的时长$D_i$(1<=$D_i$<=10000)，以及每个斜坡所需要的滑雪能力$C_i$(1<=$C_i$<=100)，以保证滑雪的安全性。Bessie的能力必须大于等于这个等级，以使得她能够安全滑下。

Bessie可以用她的时间来滑雪，上课，或者美美地喝上一杯可可汁，但是她必须在T(1<=T<=10000)时刻离开滑雪场。这意味着她必须在T时刻之前完成最后一次滑雪。

求Bessie在实现内最多可以完成多少次滑雪。这一天开始的时候，她的滑雪能力为1.

在前50个提交里，会提供额外的反馈。

Format

Input

• Line 1: Three space-separated integers: T, S, and N
• Lines 2..S+1: Line i+1 describes ski lesson i with three space-separated integers: $M_i$, $L_i$, and $A_i$
• Lines S+2..S+N+1: Line S+i+1 describes ski slope i with two space-separated integers: $C_i$ and $D_i$.

Output

A single integer on a line by itself, the maximum number of runs that Bessie may ski within the time limit.

Samples

10 1 2
3 2 5
4 1
1 3

6