Find the First Amicable Pair Not Less Than s

Given an integer s, find the first amicable pair (a, b) such that a \ge s where amicable numbers are defined as follows:

An amicable pair \((a, b)\) satisfies:

$$\sigma(a) - a = b \quad \text{and} \quad \sigma(b) - b = a$$

where \(\sigma(n)\) denotes the sum of all positive divisors of \(n\) and \(a \neq b\). For example, the smallest amicable pair is \((220, 284)\) because:

• \(\sigma(220)-220 = 284\)
• \(\sigma(284)-284 = 220\)

Your task is to find and output the first amicable pair \((a, b)\) with \(a \ge s\).

inputFormat

The input consists of a single integer s (\(1 \le s \le 10^5\)).

outputFormat

Output two space-separated integers, \(a\) and \(b\), representing the first amicable pair with \(a \ge s\).

sample

200

220 284