Conjecture

#include <algorithm>
#include <iostream>
#include <iterator>
#include <numeric>
#include <sstream>
#include <fstream>
#include <cassert>
#include <climits>
#include <cstdlib>
#include <cstring>
#include <string>
#include <cstdio>
#include <vector>
#include <bitset>
#include <cmath>
#include <queue>
#include <deque>
#include <stack>
#include <list>
#include <map>
#include <set>

using namespace std;

#define ll long long
#define ld long double
#define ii pair<int,int>
#define si pair<string,int>
#define iii pair<int,ii>
#define vi vector<int>
#define vc vector<char>
#define vs vector<string>
#define msvs map<string,vs>
#define msi map<string,int>
#define mss map<string,int>
#define us unordered_set
#define um unordered_map
#define pq priority_queue
#define pb push_back
#define mp make_pair
#define forall(i,a,b) for (int i=a;i<b;i++)
#define foreach(v,c) for( typeof( (c).begin()) v = (c).begin();  v != (c).end(); ++v)
#define all(a) a.begin(), a.end()
#define in(a,b) ( (b).find(a) != (b).end())
#define fill(a,v) memset(a, v, sizeof a)
#define sz(a) ((int)(a.size()))
#define N (1<<17)
#define M 1000000007
#define I 500000004
int main()
{
	cin.sync_with_stdio(false);
	ll n; cin >> n;
	if (n < 7) {
		cout << 7 << "\n";
	} else if (n == 7) {
		cout << 8 << "\n";
	} else if (n%3 == 0) {
		cout << n+1 << "\n";
	} else if (n%3 == 1) {
		cout << n+1 << "\n";
	} else if (n%3 == 2) {
		cout << n+2 << "\n";
	}
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED