A. Guess the Maximum

Alice and Bob came up with a rather strange game. They have an array of integers 𝑎1,𝑎2,…,𝑎𝑛. Alice chooses a certain integer 𝑘 and tells it to Bob, then the following happens:

• Bob chooses two integers 𝑖 and 𝑗 (1≤𝑖<𝑗≤𝑛), and then finds the maximum among the integers 𝑎𝑖,𝑎𝑖+1,…,𝑎𝑗;
• If the obtained maximum is strictly greater than 𝑘, Alice wins, otherwise Bob wins.

Help Alice find the maximum 𝑘 at which she is guaranteed to win.