P1663 Mountain

Given a mountain as shown in the figure.  You need to place a lamp somewhere on the mountain so that every part of the mountain is visible. Output the minimum $y$-coordinate. As shown, the `+` mark indicates the installation point with the minimum $y$-coordinate.

The first line contains an integer $N$, indicating that the mountain consists of $N$ points. The next $N$ lines, from left to right, describe the mountain. Each line contains two numbers $X_i, Y_i$ representing a vertex, and it is guaranteed that $X_i > X_{i-1}$.

Output a single line with the minimum $y$-coordinate. Your answer is considered correct if it differs from the standard answer by no more than $0.01$.

Constraints: $30 \%$ of the testdata, $1 \le N \le 50$. $100 \%$ of the testdata, $1 \le N \le 5000$; $0 \le X_i, Y_i \le 100000$, and the answer is guaranteed to be no more than $1000000$. Translated by ChatGPT 5