Problem:
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The Number of Inversions

For a given sequence $A = \{a_0, a_1, ... a_{n-1}\}$, the number of pairs $(i, j)$ where $a_i > a_j$ and $i < j$, is called the number of inversions. The number of inversions is equal to the number of swaps of Bubble Sort defined in the following program:

bubbleSort(A)
cnt = 0 // the number of inversions
for i = 0 to A.length-1
for j = A.length-1 downto i+1
if A[j] < A[j-1]
swap(A[j], A[j-1])
cnt++

return cnt

For the given sequence $A$, print the number of inversions of $A$. Note that you should not use the above program, which brings Time Limit Exceeded.

Input

In the first line, an integer $n$, the number of elements in $A$, is given. In the second line, the elements $a_i$ ($i = 0, 1, .. n-1$) are given separated by space characters.

output

Print the number of inversions in a line.

Constraints

$ 1 \leq n \leq 200,000$

$ 0 \leq a_i \leq 10^9$

$a_i$ are all different

Sample Input 1

5
3 5 2 1 4

Sample Output 1

6

Sample Input 2

3
3 1 2

Sample Output 2

2

Solution in JAVA (judge verdict: Accepted)

import java.io.*;
import java.util.*;
import java.util.Map.Entry;
import java.util.stream.Collectors;

@SuppressWarnings("unused")
public class Main {
	
	//final boolean isDebug = true;
	final boolean isDebug = false;
	String fileName = "input.txt";
	FastScanner sc;
	PrintWriter out;
	final int MOD = (int)1e9+7;
	//final int INF = Integer.MAX_VALUE / 2;
	final long INF = Long.MAX_VALUE / 2;
	
	void solve() throws Exception{
		int n = sc.nextInt();
		int[] a = new int[n+1];
		TreeSet<Integer> ts = new TreeSet<>();
		for(int i = 1; i <= n; i++){
			a[i] = sc.nextInt();
			ts.add(a[i]);
		}
		HashMap<Integer, Integer> map = new HashMap<>();
		for(int i = 1; !ts.isEmpty(); i++) map.put(ts.pollFirst(), i);
		
		BinaryIndexedTree bit = new BinaryIndexedTree(map.size());
		long sum = 0;
		for(int i = 1; i <= n; i++){
			sum += bit.getSum(map.get(a[i]), map.size());
			bit.add(map.get(a[i]), 1);
		}
		System.out.println(sum);
	}
	
	/* end solve */
	
	/* main */
	public static void main(String[] args) throws Exception {
		new Main().m();
	}
	
	void m() throws Exception {
		long S = System.currentTimeMillis();
		sc = (isDebug) ? new FastScanner(new FileInputStream(fileName)) : new FastScanner(System.in);
		out = new PrintWriter(System.out);
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		if(isDebug){
			System.out.println("---Debug---");
			System.out.printf("%8d ms\n", (G-S));
		}
	}
	
	
	/* end main */
}
/* end Main */

class BinaryIndexedTree{
	int n;
	int[] node;
	
	/* 初期値は0 */
	public BinaryIndexedTree(int n){
		this.n = n;
		node = new int[n+1];
	}
	
	/* 1-indexed */
	public void add(int x, int val){
		for(int i = x; i <= n; i += (i & -i)){
			node[i] += val;
		}
	}
	
	/* 
	 * [1,a], 1-indexed
	 * sum(0) == 0
	 */
	public int getSum(int a){
		int res = 0;
		for(int i = a; i > 0; i -= (i & -i)){
			res += node[i];
		}
		return res;
	}
	
	/* [a,b], 1-indexed */
	public int getSum(int a, int b){
		return getSum(b) - getSum(a-1);
	}
	
	/*
	//[a,b), 1-indexed
	public int sum(int a, int b){
		return sum(b-1) - sum(a-1);
	}
	*/
	
	/*
	 * 小さいほうからk番目の値を二分探索で求める
	 * 1-indexed
	 */
	public int getKth(int k){
		if(k <= 0) return 0;
		int res = 0;
		int N = 1; while(N < node.length) N *= 2;
		for(int i = N / 2; i > 0; i /= 2){
			if(res + i < node.length && node[res + i] < k){
				k -= node[res + i];
				res += i;
			}
		}
		return res+1;
	}
}

class FastScanner {
    private InputStream in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(InputStream in) {
		this.in = in;
	}
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() {
    	if (hasNextByte()) return buffer[ptr++];
    	else return -1;
    }
    private static boolean isPrintableChar(int c){
    	return 33 <= c && c <= 126;
    }
    public boolean hasNext() {
    	while(hasNextByte() && !isPrintableChar(buffer[ptr]))
    		ptr++; return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public String nextLine() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(b != 10) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
}