D. AND, OR and square sum

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
#include <queue>
#include <map>
#include <sstream>
#include <cstdio>
#include <cstring>
#include <numeric>
#include <cmath>
#include <iomanip>
#include <deque>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#define ll              long long
#define pii             pair<int, int>
#define rep(i,a,b)      for(int  i=a;i<=b;i++)
#define dec(i,a,b)      for(int  i=a;i>=b;i--)
using namespace std;
int dir[4][2] = { { 1,0 },{ 0,1 } ,{ 0,-1 },{ -1,0 } };
const long long INF = 0x7f7f7f7f7f7f7f7f;
const int inf = 0x3f3f3f3f;
const double pi = 3.14159265358979323846;
const double eps = 1e-6;
const int mod = 1e9 + 7;
const int N = 1e3 + 5;
//if(x<0 || x>=r || y<0 || y>=c)

inline ll read()
{
    ll x = 0; bool f = true; char c = getchar();
    while (c < '0' || c > '9') { if (c == '-') f = false; c = getchar(); }
    while (c >= '0' && c <= '9') x = (x << 1) + (x << 3) + (c ^ 48), c = getchar();
    return f ? x : -x;
}
ll gcd(ll m, ll n)
{
    return n == 0 ? m : gcd(n, m % n);
}
ll lcm(ll m, ll n)
{
    return m * n / gcd(m, n);
}
bool prime(int x) {
    if (x < 2) return false;
    for (int i = 2; i * i <= x; ++i) {
        if (x % i == 0) return false;
    }
    return true;
}
ll qpow(ll m, ll k, ll mod)
{
    ll res = 1, t = m;
    while (k)
    {
        if (k & 1)
            res = res * t % mod;
        t = t * t % mod;
        k >>= 1;
    }
    return res;
}

int main()
{
    ll n;
    cin >> n;
    vector<ll> b(25),a(n+1),v(n+1);
    rep(i, 1, n)
        cin >> a[i];
    rep(i, 1, n)
    {
        for (int j = 0; j <= 20; j++)
        {
            if (a[i] & (1 << j))
                b[j]++;
        }
    }
    rep(i, 0, 20)
    {
        rep(j, 1, b[i])
        {
            v[j] += 1 << i;
        }
    }
    ll res=0;
    rep(i, 1, n)
        res += v[i] * v[i];
    cout << res << endl;
    return 0;
}

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Gottfried learned about binary number representation. He then came up with this task and presented it to you.

You are given a collection of nn non-negative integers a1,…,ana1,…,an. You are allowed to perform the following operation: choose two distinct indices 1≤i,j≤n1≤i,j≤n. If before the operation ai=xai=x, aj=yaj=y, then after the operation ai=x AND yai=x AND y, aj=x OR yaj=x OR y, where ANDAND and OROR are bitwise AND and OR respectively (refer to the Notes section for formal description). The operation may be performed any number of times (possibly zero).

After all operations are done, compute ∑ni=1a2i∑i=1nai2 — the sum of squares of all aiai. What is the largest sum of squares you can achieve?

Input

The first line contains a single integer nn (1≤n≤2⋅1051≤n≤2⋅105).

The second line contains nn integers a1,…,ana1,…,an (0≤ai<2200≤ai<220).

Output

Print a single integer — the largest possible sum of squares that can be achieved after several (possibly zero) operations.

Examples

input

Copy

1
123

output

Copy

15129

input

Copy

3
1 3 5

output

Copy

51

input

Copy

2
349525 699050

output

Copy

1099509530625

Note

In the first sample no operation can be made, thus the answer is 12321232.

In the second sample we can obtain the collection 1,1,71,1,7, and 12+12+72=5112+12+72=51.

If xx and yy are represented in binary with equal number of bits (possibly with leading zeros), then each bit of x AND yx AND y is set to 11 if and only if both corresponding bits of xx and yy are set to 11. Similarly, each bit of x OR yx OR y is set to 11 if and only if at least one of the corresponding bits of xx and yy are set to 11. For example, x=3x=3 and y=5y=5 are represented as 01120112 and 10121012 (highest bit first). Then, x AND y=0012=1x AND y=0012=1, and x OR y=1112=7x OR y=1112=7.

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