Problem:
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Maximum Profit

You can obtain profits from foreign exchange margin transactions. For example, if you buy 1000 dollar at a rate of 100 yen per dollar, and sell them at a rate of 108 yen per dollar, you can obtain (108 - 100) × 1000 = 8000 yen.

Write a program which reads values of a currency $R_t$ at a certain time $t$ ($t = 0, 1, 2, ... n-1$), and reports the maximum value of $R_j - R_i$ where $j > i$ .

Input

The first line contains an integer $n$. In the following $n$ lines, $R_t$ ($t = 0, 1, 2, ... n-1$) are given in order.

Output

Print the maximum value in a line.

Constraints

$2 \leq n \leq 200,000$

$1 \leq R_t \leq 10^9$

Sample Input 1

6
5
3
1
3
4
3

Sample Output 1

3

Sample Input 2

3
4
3
2

Sample Output 2

-1

Solution in Ruby (judge verdict: Wrong Answer)

prices = readlines.map(&:to_i)[1..-1]

profits = prices[0...-1].map.with_index { |price, index|
  profit = prices[index + 1] - price
  [profit, index]
}

positive_profits, negative_profits = profits.partition { |(profit, _)|
  profit >= 0
}

if positive_profits.empty?
  puts negative_profits.max_by { |(profit, _)| profit }.first
  exit
end

previous = nil
profit_sum = nil
max_profit = 0
positive_profits.each do |profit, index|
  previous ||= index
  profit_sum ||= 0

  if (index - previous) > 1
    max_profit = [profit_sum, max_profit].max
    previous, profit_sum = nil, nil
  else
    profit_sum += profit
    previous = index
  end
end

max_profit = [profit_sum, max_profit].max
puts max_profit