Three Equal Stretches

Easy

A cashier recorded the day's revenue changes in order in the array amounts. They want to cut the day into three non-empty contiguous stretches (morning, afternoon and evening) so that every stretch has the same sum. Return True if such a split exists, and False otherwise. Elements cannot be reordered, and each element goes into exactly one stretch.

Example 1

amounts=[4, -1, 2, 5, 0, 3, 2] → True

[4, -1, 2] = 5, [5] = 5 and [0, 3, 2] = 5.

Example 2

amounts=[1, 2, 3, 3] → True

The total is 9, so each piece must sum to 3: [1, 2], [3] and [3].

Example 3

amounts=[2, 2, 2, -3, 3] → True

The total is 6, so the pieces must sum to 2 each, e.g. [2], [2], [2, -3, 3].

Constraints

3 ≤ len(amounts) ≤ 5 · 10⁴
-10⁴ ≤ amounts[i] ≤ 10⁴

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Topics

Greedy Array

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Input

amounts=[4, -1, 2, 5, 0, 3, 2]

Expected

True

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