Back to a Dark Panel

Medium

A panel holds a row of switches numbered from zero. Each number in presses describes one press: if the number's binary form has a 1 in bit b, the press flips switch b (on ↔ off). Bit 0 is the least significant. Take a contiguous segment of presses and run it on a panel with every switch off. The segment is a *reset* if the panel ends up fully off again. Return how many reset segments presses contains.

Example 1

presses=[5, 3, 6, 1] → 1

5 = 101₂, 3 = 011₂, 6 = 110₂. The presses [5, 3, 6] flip every switch exactly twice, so the panel is dark again. No other segment does that.

Example 2

presses=[0, 4, 4] → 3

[0], [4, 4] and [0, 4, 4] qualify.

Example 3

presses=[1, 2, 4] → 0

Constraints

1 ≤ len(presses) ≤ 10⁵
0 ≤ presses[i] ≤ 10⁶

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Topics

Bit Manipulation Array Hash Table Prefix Sum

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Input

presses=[5, 3, 6, 1]

Expected

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