Define <strong>P(x)</strong> as the product of primes <strong>p</strong> with odd exponents in <strong>x</strong>'s factorization. Examples: For <code>x = 18</code>, factorization <code>2¹ × 3²</code>, <strong>P(18) = 2</strong>; for <code>x = 45</code>, factorization <code>3² × 5¹</code>, <strong>P(45) = 5</strong>; for <code>x = 50</code>, factorization <code>2¹ × 5²</code>, <strong>P(50) = 2</strong>; for <code>x = 210</code>, factorization <code>2¹ × 3¹ × 5¹ × 7¹</code>, <strong>P(210) = 210</strong>.

If <code>P(i) = P(j)</code>, <code>nums[i]</code> and <code>nums[j]</code> can be grouped together.

Pick the group with the largest sum.