Problem Statement

For a sequence $a = (a_1, a_2, a_3, \dots, a_k)$, let $f(a)$ be the sum of its elements after the following is done:

• For each $i = 1, 2, 3, \dots, k$, in this order, do the following operation: add the current maximum value of an element in $a$ to $a_i$.

You are given a sequence of length $N$: $A = (A_1, A_2, A_3, \dots, A_N)$. For each integer $k$ between $1$ and $N$ (inclusive), find $f(a)$ when $a = (A_1, A_2, A_3, \dots, A_k)$.

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le A_i \le 10^7$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 A_3 \dots A_N

Output

Print $N$ lines. The $k$-th line should contain $f(a)$ when $a = (A_1, A_2, A_3, \dots, A_k)$.