You have an array a consisting of n distinct positive integers, numbered from 1 to n. Define p_k as $$$p_k = ∑_{1 ≤ i, j ≤ k} a_i mod a_j, where x \bmod y denotes the remainder when x is divided by y. You have to find and print p_1, p_2, \ldots, p_n$$$. 

Input

The first line contains n — the length of the array (2 ≤ n ≤ 2 ⋅ 10^5).

The second line contains n space-separated distinct integers a_1, …, a_n (1 ≤ a_i ≤ 3 ⋅ 10^5, a_i ≠ a_j if i ≠ j). 

Output

Print n integers p_1, p_2, …, p_n. 

Examples

Input


4
6 2 7 3


Output


0 2 12 22


Input


3
3 2 1


Output


0 3 5
import java.io.*;
import java.util.*;

import static java.lang.Math.max;
import static java.lang.Math.min;

public class Current {
    FastScanner in;
    PrintWriter out;

    class Fenwick {
        int n;
        long[] a;

        Fenwick(int n) {
            this.n = n;
            a = new long[n + 1];
        }

        void add(int i, long x) { // 1-indexing
            while (i <= n) {
                a[i] += x;
                i = (i | (i - 1)) + 1;
            }
        }

        long prefSum(int i) { // 1-indexing
            long sum = 0;
            while (i > 0) {
                sum += a[i];
                i = i & (i - 1);
            }
            return sum;
        }

        long segSum(int l, int r) {
            return prefSum(r) - prefSum(l - 1);
        }
    }

    private void solve() throws IOException {
        int n = in.nextInt(), maxA = (int) 3e5;
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = in.nextInt();

        long pk = 0, prefSum = 0;
        Fenwick cntValue = new Fenwick(maxA);
        Fenwick cnt = new Fenwick(maxA);

        for (int k = 1; k <= n; k++) {
            pk += (long) a[k] * (k - 1);
            pk -= cntValue.prefSum(a[k]);
            for (int i = a[k]; i <= maxA; i += a[k])
                cntValue.add(i, a[k]);

            pk += prefSum;
            prefSum += a[k];
            for (int l = 0; l <= maxA; l += a[k])
                pk -= (long) l * cnt.segSum(l, min(maxA, l + a[k] - 1));
            cnt.add(a[k], 1);

            out.print(pk + (k == n ? "" : " "));
        }
        out.println();
    }

    class FastScanner {
        StringTokenizer st;
        BufferedReader br;

        FastScanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }

    private void run() throws IOException {
        in = new FastScanner(System.in);
        out = new PrintWriter(System.out);

        for (int t = 1 /* in.nextInt() */; t-- > 0; )
            solve();

        out.flush();
        out.close();
    }

    public static void main(String[] args) throws IOException {
        new Current().run();
    }
}
