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The Darkness Brought In by Swallowstone Naturalis Historia

— Dateless Bar "Old Adam"

Marisa is a girl of integrity who always helps others safeguard their belongings. Over a period of $$$n$$$ days, she comes each day to take one of Reimu's takeouts. The $$$i$$$-th takeout is described by its deliciousness value — an integer $$$w_i$$$ ($$$0\le w_i\le 2$$$), forming a sequence $$$w$$$ of length $$$n$$$.

Marisa has a special fondness for the number $$$3$$$. She can perform the following operation zero or more times:

Select a non-empty subsequence$$$^{\text{∗}}$$$ of $$$w$$$ whose sum is divisible by $$$3$$$, and remove the elements of the subsequence from $$$w$$$.

Determine the maximum number of operations Marisa can perform.

$$$^{\text{∗}}$$$A sequence $$$a$$$ is a subsequence of a sequence $$$b$$$ if $$$a$$$ can be obtained from $$$b$$$ by the deletion of several (possibly, zero or all) element from arbitrary positions.

Note

In the first test case, Marisa can perform four operations: $$$$$$[\underline{0},0,0,0]\to[\underline{0},0,0]\

Marisa Steals Reimu's Takeout

Examples