Problem:
Score : 700 points

Problem Statement

Snuke loves constructing integer sequences.

There are N piles of stones, numbered 1 through N.
The pile numbered i consists of a_i stones.

Snuke will construct an integer sequence s of length Σa_i, as follows:

Among the piles with the largest number of stones remaining, let x be the index of the pile with the smallest index. Append x to the end of s.

Select a pile with one or more stones remaining, and remove a stone from that pile.

If there is a pile with one or more stones remaining, go back to step 1. Otherwise, terminate the process.

We are interested in the lexicographically smallest sequence that can be constructed. For each of the integers 1,2,3,...,N, how many times does it occur in the lexicographically smallest sequence?

Constraints

1 ≤ N ≤ 10^{5}

1 ≤ a_i ≤ 10^{9}

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_{N}

Output

Print N lines. The i-th line should contain the number of the occurrences of the integer i in the lexicographically smallest sequence that can be constructed.

Sample Input 1

2
1 2

Sample Output 1

2
1

The lexicographically smallest sequence is constructed as follows:

Since the pile with the largest number of stones remaining is pile 2, append 2 to the end of s. Then, remove a stone from pile 2.

Since the piles with the largest number of stones remaining are pile 1 and 2, append 1 to the end of s (we take the smallest index). Then, remove a stone from pile 2.

Since the pile with the largest number of stones remaining is pile 1, append 1 to the end of s. Then, remove a stone from pile 1.

The resulting sequence is (2,1,1). In this sequence, 1 occurs twice, and 2 occurs once.

Sample Input 2

10
1 2 1 3 2 4 2 5 8 1

Sample Output 2

10
7
0
4
0
3
0
2
3
0

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::{self, Stdin};
use std::str::{self, FromStr};
use std::error::Error;
use std::thread;
use std::cmp::*;
fn exec() {
    let mut sc = Scanner::new();
    let n: usize = sc.ne();
    let a: Vec<i64> = (0..n).map(|_| sc.ne()).collect();
    let mut z: Vec<_> = a.into_iter().zip(0..).collect();
    z.push((0, -1));
    z.sort();
    let mut ans = vec![0; n];
    let (mut mi, mut cnt, mut mx) = (n, 0, z[n].0);
    for (x, i) in z.into_iter().rev() {
        if x != mx {
            assert!(mi < n);
            ans[mi] += (mx - x) * cnt;
            mx = x;
        }
        cnt += 1;
        mi = min(mi, i as usize);
    }
    for x in ans {
        println!("{}", x);
    }
}

fn main() {
    const DEFAULT_STACK: usize = 16 * 1024 * 1024;
    let builder = thread::Builder::new();
    let th = builder.stack_size(DEFAULT_STACK);
    let handle = th.spawn(|| { exec(); }).unwrap();
    let _ = handle.join();
}

trait Monoid<T>: Clone {
    fn merge(&T, &T) -> T;
    fn ide() -> T;
}

// Range Minimum Query
type Int = i64;
impl Monoid<Int> for Int {
    fn merge(l: &Int, r: &Int) -> Int {
        std::cmp::min(*l, *r)
    }
    fn ide() -> Int {
        std::i32::MAX as Int
    }
}

#[allow(dead_code)]
struct Scanner {
    stdin: Stdin,
    id: usize,
    buf: Vec<u8>,
}

#[allow(dead_code)]
impl Scanner {
    fn new() -> Scanner {
        Scanner {
            stdin: io::stdin(),
            id: 0,
            buf: Vec::new(),
        }
    }
    fn next_line(&mut self) -> Option<String> {
        let mut res = String::new();
        match self.stdin.read_line(&mut res) {
            Ok(0) => return None,
            Ok(_) => Some(res),
            Err(why) => panic!("error in read_line: {}", why.description()),
        }
    }
    fn next<T: FromStr>(&mut self) -> Option<T> {
        while self.buf.len() == 0 {
            self.buf = match self.next_line() {
                Some(r) => {
                    self.id = 0;
                    r.trim().as_bytes().to_owned()
                }
                None => return None,
            };
        }
        let l = self.id;
        assert!(self.buf[l] != b' ');
        let n = self.buf.len();
        let mut r = l;
        while r < n && self.buf[r] != b' ' {
            r += 1;
        }
        let res = match str::from_utf8(&self.buf[l..r]).ok().unwrap().parse::<T>() {
            Ok(s) => Some(s),
            Err(_) => {
                panic!("parse error, {:?}",
                       String::from_utf8(self.buf[l..r].to_owned()))
            }
        };
        while r < n && self.buf[r] == b' ' {
            r += 1;
        }
        if r == n {
            self.buf.clear();
        } else {
            self.id = r;
        }
        res
    }
    fn ne<T: FromStr>(&mut self) -> T {
        self.next::<T>().unwrap()
    }
}