E. Tourists
data structures; dfs and similar; graphs; trees
There are n cities in Cyberland, numbered from 1 to n, connected by m bidirectional roads. The j-th road connects city aj and bj.For tourists, souvenirs are sold in every city of Cyberland. In particular, city i sell it at a price of wi.Now there are q queries for you to handle. There are two types of queries: ""C a w"": The price in city a is changed to w. ""A a b"": Now a tourist will travel from city a to b. He will choose a route, he also doesn't want to visit a city twice. He will buy souvenirs at the city where the souvenirs are the cheapest (possibly exactly at city a or b). You should output the minimum possible price that he can buy the souvenirs during his travel.More formally, we can define routes as follow: A route is a sequence of cities [x1, x2, ..., xk], where k is a certain positive integer. For any 1 ≤ i < j ≤ k, xi ≠ xj. For any 1 ≤ i < k, there is a road connecting xi and xi + 1. The minimum price of the route is min(wx1, wx2, ..., wxk). The required answer is the minimum value of the minimum prices of all valid routes from a to b.
The first line of input contains three integers n, m, q (1 ≤ n, m, q ≤ 105), separated by a single space.Next n lines contain integers wi (1 ≤ wi ≤ 109).Next m lines contain pairs of space-separated integers aj and bj (1 ≤ aj, bj ≤ n, aj ≠ bj).It is guaranteed that there is at most one road connecting the same pair of cities. There is always at least one valid route between any two cities.Next q lines each describe a query. The format is ""C a w"" or ""A a b"" (1 ≤ a, b ≤ n, 1 ≤ w ≤ 109).
For each query of type ""A"", output the corresponding answer.
For the second sample, an optimal routes are:From 2 to 3 it is [2, 3].From 6 to 4 it is [6, 5, 1, 2, 4].From 6 to 7 it is [6, 5, 7].From 3 to 3 it is [3].