Restaurant Bribes

Eeet is a social service for sharing restaurant ratings. A member can rate a restaurant with an integer from $0$ to $10$, or leave no rating at all. The score a member sees for a restaurant is the average of the ratings left by the friends who rated it. A friend who leaves a $0$ usually drags that score down, while a friend who leaves no rating does not change it. A restaurant that none of a member's friends rated does not show up for that member.

The Smelly Fish is a new restaurant, and nobody eats there. The owners found out that each person comes at most once and spends $100y$ SEK on that visit, where $y$ is the score that person sees on Eeet. Everybody pays by card, and the amounts are not rounded.

There are no ratings yet, so the owners picked a few people to bribe for a rating. A person with parameter $a$ who receives a bribe of $x$ SEK leaves the rating $\min(10, \lfloor \sqrt{x}/a \rfloor)$. A person bribed with $0$ SEK still leaves a rating of $0$ instead of leaving no rating. A bribed person knows about the scheme and never comes to the restaurant. The owners pick the bribe for each of these people separately, and a bribe can be any nonnegative real amount.

The profit is the money the customers spend minus the money paid out in bribes. Compute the largest profit the owners can reach.

The first line contains three integers $n$, $m$, and $k$ ($1 \le n \le 10^5$, $0 \le m \le 10^5$, $0 \le k \le n$): the number of people on Eeet, the number of friendships, and the number of people to bribe. People are numbered from $1$ to $n$.

Each of the next $m$ lines contains two integers $a$ and $b$ ($1 \le a, b \le n$, $a \ne b$), the ids of a pair of friends. Friendship holds both ways, and no unordered pair $\{a, b\}$ is given twice.

Each of the next $k$ lines contains two integers $i$ and $a_i$ ($1 \le i \le n$, $1 \le a_i \le 1000$), the id of a person to bribe and that person's parameter. No id is given twice. Every person on this list is bribed, possibly with $0$ SEK.

Print the maximum profit exactly, as a fraction in lowest terms. If the profit is an integer, print that integer by itself. Otherwise print $p/q$ with no spaces, where $q \ge 2$ and $\gcd(p, q) = 1$. The numerator and the denominator can run far past the $64$-bit range, so use exact big-integer arithmetic.