Problem: It was the third month of remote learning, Nastya got sick of staying at dormitory, so she decided to return to her hometown. In order to make her trip more entertaining, one of Nastya's friend presented her an integer array a. 

Several hours after starting her journey home Nastya remembered about the present. To entertain herself she decided to check, are there four different indices x, y, z, w such that a_x + a_y = a_z + a_w.

Her train has already arrived the destination, but she still hasn't found the answer. Can you help her unravel the mystery?

Input

The first line contains the single integer n (4 ≤ n ≤ 200 000) — the size of the array.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 2.5 ⋅ 10^6).

Output

Print "YES" if there are such four indices, and "NO" otherwise.

If such indices exist, print these indices x, y, z and w (1 ≤ x, y, z, w ≤ n).

If there are multiple answers, print any of them.

Examples

Input


6
2 1 5 2 7 4


Output


YES
2 3 1 6 

Input


5
1 3 1 9 20


Output


NO

Note

In the first example a_2 + a_3 = 1 + 5 = 2 + 4 = a_1 + a_6. Note that there are other answer, for example, 2 3 4 6.

In the second example, we can't choose four indices. The answer 1 2 2 3 is wrong, because indices should be different, despite that a_1 + a_2 = 1 + 3 = 3 + 1 = a_2 + a_3

Solution (in CPP):

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

/* 
find my code templates at https://github.com/galencolin/cp-templates
also maybe subscribe please thanks 
*/
 
#define send {ios_base::sync_with_stdio(false);}
#define help {cin.tie(NULL);}
#define f first
#define s second
#define getunique(v) {sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end());}
typedef long long ll;
typedef long double lld;
typedef unsigned long long ull;
 
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v);
template<typename A, typename B> ostream& operator<<(ostream &cout, pair<A, B> const &p) { return cout << "(" << p.f << ", " << p.s << ")"; }
template<typename A> ostream& operator<<(ostream &cout, vector<A> const &v) {
	cout << "["; for(int i = 0; i < v.size(); i++) {if (i) cout << ", "; cout << v[i];} return cout << "]";
}
template<typename A, typename B> istream& operator>>(istream& cin, pair<A, B> &p) {
	cin >> p.first;
	return cin >> p.second;
}
 
mt19937_64 rng(std::chrono::steady_clock::now().time_since_epoch().count());
// mt19937_64 rng(61378913);
/* usage - just do rng() */
 
void usaco(string filename) {
  // #pragma message("be careful, freopen may be wrong")
	freopen((filename + ".in").c_str(), "r", stdin);
	freopen((filename + ".out").c_str(), "w", stdout);
}
 
// #include <atcoder/all>
// using namespace atcoder;
 
const lld pi = 3.14159265358979323846;
// const ll mod = 1000000007;
// const ll mod = 998244353;
// ll mod;



ll n, m, k, q, l, r, x, y, z;
const ll template_array_size = 1e6 + 8432;
ll a[template_array_size];
ll b[template_array_size];
ll c[template_array_size];
string s, t;
ll ans = 0;	

pair<ll, ll> p[200005];
vector<pair<ll, ll>> cv;
map<ll, ll> cnt;
ll tot[5000005];

void solve(int tc = 0) {
	cin >> n;
	for (ll i = 0; i < n; i++) {
		cin >> a[i];
		p[i] = {a[i], i};
		++cnt[a[i]];
	}
	
	sort(p, p + n);
	
	ll targ = -1;
	for (pair<ll, ll> x: cnt) cv.push_back(x);
	for (ll i = 0; i < cv.size(); i++) {
		tot[2 * cv[i].f] += cv[i].s / 2;
		if (tot[2 * cv[i].f] > 1) {
			targ = 2 * cv[i].f;
			break;
		}
		for (ll j = i + 1; j < cv.size(); j++) {
			tot[cv[i].f + cv[j].f] += min(cv[i].s, cv[j].s);
			if (tot[cv[i].f + cv[j].f] > 1) {
				targ = cv[i].f + cv[j].f;
				break;
			}
		}
		if (targ != -1) break;
	}
	
	if (targ == -1) {
		cout << "NO\n";
	} else {
		cout << "YES\n";
		ll pt = n - 1;
		ll t = 0;
		for (ll i = 0; i < n; i++) {
			while (pt > i && p[i].f + p[pt].f > targ) --pt;
			if (pt > i && p[i].f + p[pt].f == targ) {
				cout << p[i].s + 1 << " " << p[pt].s + 1 << " ";
				--pt;
				++t;
				if (t == 2) exit(0);
			}
		}
	}
}

// two pointers? maybe
// xor tricks (or general bitwise)
// tutorial on my template

int main() {
	#ifdef galen_colin_local
		auto begin = std::chrono::high_resolution_clock::now();
	#endif
	
	send help
 
	#ifndef galen_colin_local
		// usaco("code");
	#endif
	
	// usaco("cowland");
	
	// freopen("tc.cpp", "r", stdin);
	// freopen("tc2.cpp", "w", stdout);
 		
	cout << setprecision(15) << fixed;
					
	int tc = 1;
	// cin >> tc;
	for (int t = 0; t < tc; t++) solve(t);
	
	#ifdef galen_colin_local
		auto end = std::chrono::high_resolution_clock::now();
		cerr << setprecision(4) << fixed;
		// cerr << "Execution time: " << std::chrono::duration_cast<std::chrono::duration<double>>(end - begin).count() << " seconds" << endl;
	#endif
}