Balanced Array

ArrayDynamic ProgrammingPrefix Sum

Given an array of non-negative integers, determine if the array can be split into two parts such that the sum of elements in both parts is the same. Return true if it can be split equally, otherwise return false.

Example 1

Input

Output

true

Explanation. The array can be split into [1, 5, 5] and [11] where both have the sum of 11.

Example 2

Input

Output

false

Explanation. There is no possible way to split this array into two parts with an equal sum.

Example 3

Input

Output

true

Explanation. The array can be split into [10, 10] and [10, 10] where both have the sum of 20.

Example 4

Input

Output

true

Explanation. The array can be split into [1, 1, 1, 1] and [2] where both have the sum of 4.

Example 5

Input

Output

false

Explanation. There is no possible way to split this array into two parts with an equal sum.

Follow-up: Can you solve the problem in linear time O(n) and constant space O(1)?

Constraints:

The input array will contain at least one element and all elements will be non-negative integers.

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