How to write "not for anything"?

In response to gratitude, we often say "not for anything", wanting to express that for you it's nothing, do not worry. But what if you have to give such an answer in writing?

How correctly to write: "not for what" or "nezachto"? According to the rules of the Russian language, namely the rule on the spelling of particles "not" and "neither", the particle "not" is spelled separately in pronouns, when it is separated from the pronoun by some pretext. For example: not for anything, nothing, no one, no one. And if there is no preposition between them, then the particle "not" will be written together. For example: someone, nothing, no one.

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