入出力高速化

#Purpose

cin/cout automatically flushes the buffer to ensure the execution order matches C-style stdio output. This disables that behavior. It also configures output precision to 16 decimal places.
To avoid writing it inside main(), we use a technique of calling it as a struct constructor:

#Implementation

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struct init {
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  init() {
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    cin.tie(0)->sync_with_stdio(0);
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    ios::sync_with_stdio(false);
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    cout << fixed << setprecision(16);
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  }
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} init;