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
/**
 * author: derrick20
 * created: 7/25/21 3:12 PM
 */
import java.io.*;
import java.util.*;
import static java.lang.Math.*;

public class F_PairwiseModulo {
    static FastScanner sc = new FastScanner();
    static PrintWriter out = new PrintWriter(System.out);
    
    public static void main(String[] args) {
        int MAX = (int) 3e5;
        int N = sc.nextInt();
        BIT pullContrib = new BIT(MAX);
        RangeBIT pushContrib = new RangeBIT(MAX);
        long pre = 0;
        long ans = 0;
        for (int i = 0; i < N; i++) {
            int a = sc.nextInt();
            long rightAmt = pre + (long) a * i;
            pre += a;
            rightAmt -= pushContrib.query(a) - pushContrib.query(a - 1);
            for (int b = a; b <= MAX; b += a) {
                long blockCount = pullContrib.get(min(b + a - 1, MAX)) - pullContrib.get(b - 1);
                rightAmt -= b * blockCount;
                pushContrib.addRange(b, min(b + a - 1, MAX), b);
            }
            pullContrib.add(a, 1);
            ans += rightAmt;
            out.print(ans + " ");
        }
        out.println();
        out.close();
    }

    static class BIT {
        long[] tree;
        public BIT(int max) {
            tree = new long[max + 1];
        }

        public void add(int i, long delta) {
            while (0 < i && i < tree.length) {
                tree[i] += delta;
                i += i & -i;
            }
        }

        public long get(int i) {
            long ans = 0;
            while (i > 0) {
                ans += tree[i];
                i -= i & -i;
            }
            return ans;
        }
    }

    static class RangeBIT {
        long[] linearTree, constantTree;
        public RangeBIT(int max) {
            linearTree = new long[max + 1];
            constantTree = new long[max + 1];
        }

        public void add(boolean doLinear, int i, long delta) {
            long[] tree = doLinear ? linearTree : constantTree;
            if (i == 0) return;
            while (i < tree.length) {
                tree[i] += delta;
                i += i & -i;
            }
        }

        public void addRange(int l, int r, long delta) {
            if (l > r) return;
            add(true, l, delta);
            add(true, r + 1, -delta);
            add(false, l, delta * (-l + 1));
            add(false, r + 1, delta * r);
        }

        public long query(int i) {
            long constant = 0;
            long coeff = 0;
            int j = i;
            while (j > 0) {
                constant += constantTree[j];
                coeff += linearTree[j];
                j -= j & -j;
            }
            return coeff * i + constant;
        }
    }

    static class FastScanner {
        private int BS = 1 << 16;
        private char NC = (char) 0;
        private byte[] buf = new byte[BS];
        private int bId = 0, size = 0;
        private char c = NC;
        private double cnt = 1;
        private BufferedInputStream in;
    
        public FastScanner() {
            in = new BufferedInputStream(System.in, BS);
        }
    
        public FastScanner(String s) {
            try {
                in = new BufferedInputStream(new FileInputStream(new File(s)), BS);
            } catch (Exception e) {
                in = new BufferedInputStream(System.in, BS);
            }
        }
    
        char getChar() {
            while (bId == size) {
                try {
                    size = in.read(buf);
                } catch (Exception e) {
                    return NC;
                }
                if (size == -1) return NC;
                bId = 0;
            }
            return (char) buf[bId++];
        }
    
        int nextInt() {
            return (int) nextLong();
        }
    
        long nextLong() {
            cnt = 1;
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            long res = 0;
            for (; c >= '0' && c <= '9'; c = getChar()) {
                res = (res << 3) + (res << 1) + c - '0';
                cnt *= 10;
            }
            return neg ? -res : res;
        }
    
        double nextDouble() {
            boolean neg = false;
            if (c == NC) c = getChar();
            for (; (c < '0' || c > '9'); c = getChar()) {
                if (c == '-') neg = true;
            }
            double cur = nextLong();
            if (c != '.') {
                return neg ? -cur : cur;
            } else {
                double frac = nextLong() / cnt;
                return neg ? -cur - frac : cur + frac;
            }
        }
    
        String next() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c > 32) {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
    
        String nextLine() {
            StringBuilder res = new StringBuilder();
            while (c <= 32) c = getChar();
            while (c != '\n') {
                res.append(c);
                c = getChar();
            }
            return res.toString();
        }
    
        boolean hasNext() {
            if (c > 32) return true;
            while (true) {
                c = getChar();
                if (c == NC) return false;
                else if (c > 32) return true;
            }
        }
    }
    
    static void ASSERT(boolean assertion, String message) {
        if (!assertion) throw new AssertionError(message);
    }
    
    static void ASSERT(boolean assertion) {
        if (!assertion) throw new AssertionError();
    }
}