Grown From "abc"

Medium

Start with an empty string. In one step you may insert the three letters "abc" together anywhere in the current string: at the start, at the end, or between any two characters. Given a string text, return true if it can be built by such steps, and false otherwise.

Example 1

text="ababcc" → True

"" → "abc" → "ab" + "abc" + "c" = "ababcc".

Example 2

text="abcabcabc" → True

Three inserts of "abc", each at the end.

Example 3

text="acbabc" → False

Removing the trailing "abc" leaves "acb", which no sequence of inserts can produce.

Constraints

1 ≤ len(text) ≤ 2 · 10⁵
text consists only of the letters a, b and c

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Input

text="ababcc"

Expected

True

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