Ivan Anatolyevich's agency is starting to become famous in the town. 

They have already ordered and made *n* TV commercial videos. Each video is made in a special way: the colors and the soundtrack are adjusted to the time of the day and the viewers' mood. That's why the *i*-th video can only be shown within the time range of [*l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub>] (it is not necessary to use the whole segment but the broadcast time should be within this segment).

Now it's time to choose a TV channel to broadcast the commercial. Overall, there are *m* TV channels broadcasting in the city, the *j*-th one has *c*<sub class="lower-index">*j*</sub> viewers, and is ready to sell time [*a*<sub class="lower-index">*j*</sub>, *b*<sub class="lower-index">*j*</sub>] to broadcast the commercial.

Ivan Anatolyevich is facing a hard choice: he has to choose exactly one video *i* and exactly one TV channel *j* to broadcast this video and also a time range to broadcast [*x*, *y*]. At that the time range should be chosen so that it is both within range [*l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub>] and within range [*a*<sub class="lower-index">*j*</sub>, *b*<sub class="lower-index">*j*</sub>].

Let's define the efficiency of the broadcast as value (*y* - *x*)·*c*<sub class="lower-index">*j*</sub> — the total sum of time that all the viewers of the TV channel are going to spend watching the commercial. Help Ivan Anatolyevich choose the broadcast with the maximum efficiency!
The first line contains two integers *n* and *m* (1 ≤ *n*, *m* ≤ 2·10<sup class="upper-index">5</sup>) — the number of commercial videos and channels, respectively.

Each of the following *n* lines contains two integers *l*<sub class="lower-index">*i*</sub>, *r*<sub class="lower-index">*i*</sub> (0 ≤ *l*<sub class="lower-index">*i*</sub> ≤ *r*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">9</sup>) — the segment of time when it is possible to show the corresponding video.

Each of the following *m* lines contains three integers *a*<sub class="lower-index">*j*</sub>, *b*<sub class="lower-index">*j*</sub>, *c*<sub class="lower-index">*j*</sub> (0 ≤ *a*<sub class="lower-index">*j*</sub> ≤ *b*<sub class="lower-index">*j*</sub> ≤ 10<sup class="upper-index">9</sup>, 1 ≤ *c*<sub class="lower-index">*j*</sub> ≤ 10<sup class="upper-index">9</sup>), characterizing the TV channel.
print("_RANDOM_GUESS_1689422808.058577")# 1689422808.058594