New Year is coming in Tree World! In this world, as the name implies, there are *n* cities connected by *n* - 1 roads, and for any two distinct cities there always exists a path between them. The cities are numbered by integers from 1 to *n*, and the roads are numbered by integers from 1 to *n* - 1. Let's define *d*(*u*, *v*) as total length of roads on the path between city *u* and city *v*.

As an annual event, people in Tree World repairs exactly one road per year. As a result, the length of one road decreases. It is already known that in the *i*-th year, the length of the *r*<sub class="lower-index">*i*</sub>-th road is going to become *w*<sub class="lower-index">*i*</sub>, which is shorter than its length before. Assume that the current year is year 1.

Three Santas are planning to give presents annually to all the children in Tree World. In order to do that, they need some preparation, so they are going to choose three distinct cities *c*<sub class="lower-index">1</sub>, *c*<sub class="lower-index">2</sub>, *c*<sub class="lower-index">3</sub> and make exactly one warehouse in each city. The *k*-th (1 ≤ *k* ≤ 3) Santa will take charge of the warehouse in city *c*<sub class="lower-index">*k*</sub>.

It is really boring for the three Santas to keep a warehouse alone. So, they decided to build an only-for-Santa network! The cost needed to build this network equals to *d*(*c*<sub class="lower-index">1</sub>, *c*<sub class="lower-index">2</sub>) + *d*(*c*<sub class="lower-index">2</sub>, *c*<sub class="lower-index">3</sub>) + *d*(*c*<sub class="lower-index">3</sub>, *c*<sub class="lower-index">1</sub>) dollars. Santas are too busy to find the best place, so they decided to choose *c*<sub class="lower-index">1</sub>, *c*<sub class="lower-index">2</sub>, *c*<sub class="lower-index">3</sub> randomly uniformly over all triples of distinct numbers from 1 to *n*. Santas would like to know the expected value of the cost needed to build the network.

However, as mentioned, each year, the length of exactly one road decreases. So, the Santas want to calculate the expected after each length change. Help them to calculate the value.
The first line contains an integer *n* (3 ≤ *n* ≤ 10<sup class="upper-index">5</sup>) — the number of cities in Tree World.

Next *n* - 1 lines describe the roads. The *i*-th line of them (1 ≤ *i* ≤ *n* - 1) contains three space-separated integers *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub>, *l*<sub class="lower-index">*i*</sub> (1 ≤ *a*<sub class="lower-index">*i*</sub>, *b*<sub class="lower-index">*i*</sub> ≤ *n*, *a*<sub class="lower-index">*i*</sub> ≠ *b*<sub class="lower-index">*i*</sub>, 1 ≤ *l*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">3</sup>), denoting that the *i*-th road connects cities *a*<sub class="lower-index">*i*</sub> and *b*<sub class="lower-index">*i*</sub>, and the length of *i*-th road is *l*<sub class="lower-index">*i*</sub>.

The next line contains an integer *q* (1 ≤ *q* ≤ 10<sup class="upper-index">5</sup>) — the number of road length changes.

Next *q* lines describe the length changes. The *j*-th line of them (1 ≤ *j* ≤ *q*) contains two space-separated integers *r*<sub class="lower-index">*j*</sub>, *w*<sub class="lower-index">*j*</sub> (1 ≤ *r*<sub class="lower-index">*j*</sub> ≤ *n* - 1, 1 ≤ *w*<sub class="lower-index">*j*</sub> ≤ 10<sup class="upper-index">3</sup>). It means that in the *j*-th repair, the length of the *r*<sub class="lower-index">*j*</sub>-th road becomes *w*<sub class="lower-index">*j*</sub>. It is guaranteed that *w*<sub class="lower-index">*j*</sub> is smaller than the current length of the *r*<sub class="lower-index">*j*</sub>-th road. The same road can be repaired several times.
print("_RANDOM_GUESS_1689259659.063702")# 1689259659.0637171