Person in charge

• 035966_L3

Problem Description

There are $n$ non-negative integers $a_1,a_2,\ldots,a_n$, where each $a_i$ takes a value between $0$ and $15$, inclusive.

Before interaction begins, you can obtain the value of $n$.

You have $4$ interaction opportunities. In each interaction, you can specify a non-negative integer $x$ (must be between $0$ and $15$ inclusive), and you will receive the count of elements in $a_1,a_2,\ldots,a_n$ that satisfy $a_i \text{ AND } x = a_i$.

Using these $4$ interactions, determine the value of $a_1 + a_2 + \ldots + a_n$.

Interaction Protocol

This is an interactive problem.

The problem provides an additional header file "conversion.h" for interaction:

Use the following template:

#include <bits/stdc++.h>
#include "conversion.h"
using namespace std;
int main()
{
  int n = start(); // Get n
  int s = 0; // Answer
  // Perform interactions here using interact()
  stop(s); // Submit answer
  return 0;
}

Sample

For this sample, $n=4$, $\{a_4\}=\{0,1,2,3\}$, with correct answer $0+1+2+3=6$.

The following interaction sequence would get AC:

Constraints

$1 \le n \le 10^6,0 \le a_i \le 15.$