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3875. Construct Uniform Parity Array I

You are given an array nums1 of n distinct integers.

You want to construct another array nums2 of length n such that the elements in nums2 are either all odd or all even.

For each index i, you must choose exactly one of the following (in any order):

  • nums2[i] = nums1[i]
  • nums2[i] = nums1[i] - nums1[j], for an index j != i

Return true if it is possible to construct such an array, otherwise, return false.

Example 1

Input: nums1 = [2,3]
Output: true
Explanation:
Choose nums2[0] = nums1[0] - nums1[1] = 2 - 3 = -1.
Choose nums2[1] = nums1[1] = 3.
nums2 = [-1, 3], and both elements are odd. Thus, the answer is true.

Example 2

Input: nums1 = [4,6]
Output: true
Explanation:
Choose nums2[0] = nums1[0] = 4.
Choose nums2[1] = nums1[1] = 6.
nums2 = [4, 6], and all elements are even. Thus, the answer is true.

Constraints

  • 1 <= n == nums1.length <= 100
  • 1 <= nums1[i] <= 100
  • nums1 consists of distinct integers.