1478C - Nezzar and Symmetric Array - CodeForces Solution

// Source: https://usaco.guide/general/io

#include <bits/stdc++.h>
using namespace std;

int main() {
	int t; cin >> t;
	while(t--){
		bool possible=true;
		long long n; cin >> n;
		vector<long long> diffs(2*n);
		for(auto &x:diffs) cin >> x;
		sort(diffs.begin(), diffs.end());
		for(int i=0;i<n;i++){
			if(diffs[2*i]!=diffs[2*i+1]) possible=false;
			if(0<i&&(diffs[2*i]==diffs[2*(i-1)])) possible=false;
		}
		long long sum=0;
		for(long long i=n*2-1;i>=1;i-=2){
			long long curr=(diffs[i]-2*sum)/(2*n);
			if(curr<=0||(2*n*curr+2*sum)!=diffs[i]){
				possible=false;
			}
			sum+=curr;
			n--;
			if(!possible) break;
		}
		if(possible) cout << "YES\n";
		else cout << "NO\n";
	}
}