human
Can you provide a Python program to print n integers, a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9), such that if you calculate x according to the statement, b_1 will be equal to a_1 - x_1, b_2 will be equal to a_2 - x_2, given the following:
Alicia has an array, a_1, a_2, …, a_n, of non-negative integers. For each 1 ≤ i ≤ n, she has found a non-negative integer x_i = max(0, a_1, …, a_{i-1}). Note that for i=1, x_i = 0.

For example, if Alicia had the array a = \{0, 1, 2, 0, 3\}, then x = \{0, 0, 1, 2, 2\}.

Then, she calculated an array, b_1, b_2, …, b_n: b_i = a_i - x_i.

For example, if Alicia had the array a = \{0, 1, 2, 0, 3\}, b = \{0-0, 1-0, 2-1, 0-2, 3-2\} = \{0, 1, 1, -2, 1\}.

Alicia gives you the values b_1, b_2, …, b_n and asks you to restore the values a_1, a_2, …, a_n. Can you help her solve the problem?

Input

The first line contains one integer n (3 ≤ n ≤ 200 000) – the number of elements in Alicia's array.

The next line contains n integers, b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9).

It is guaranteed that for the given array b there is a solution a_1, a_2, …, a_n, for all elements of which the following is true: 0 ≤ a_i ≤ 10^9.

Output

Print n integers, a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9), such that if you calculate x according to the statement, b_1 will be equal to a_1 - x_1, b_2 will be equal to a_2 - x_2, ..., and b_n will be equal to a_n - x_n.

It is guaranteed that there exists at least one solution for the given tests. It can be shown that the solution is unique.

Examples

Input

5
0 1 1 -2 1

Output

0 1 2 0 3 

Input

3
1000 999999000 -1000000000

Output

1000 1000000000 0 

Input

5
2 1 2 2 3

Output

2 3 5 7 10 

Note

The first test was described in the problem statement.

In the second test, if Alicia had an array a = \{1000, 1000000000, 0\}, then x = \{0, 1000, 1000000000\} and b = \{1000-0, 1000000000-1000, 0-1000000000\} = \{1000, 999999000, -1000000000\}.
Using python3 can you solve the prior task?
assistant
#Here is Python program to print n integers, a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9), such that if you calculate x according to the statement, b_1 will be equal to a_1 - x_1, b_2 will be equal to a_2 - x_2, .

# region smaller_fastio
from sys import stdin, stdout
from os import path

if (path.exists('input.txt')):
    # ------------------Sublime--------------------------------------#
    stdin = open('input.txt', 'r');
    stdout = open('output.txt', 'w');

    def I():
        return (int(input()))

    def In():
        return (map(int, input().split()))
else:
    # ------------------PYPY FAst I/o--------------------------------#
    def I():
        return (int(stdin.readline()))

    def In():
        return (map(int, stdin.readline().split()))

    def S():
        return (stdin.readline().rstrip())

    def Sn():
        return (stdin.readline().split(' '))

# endregion

def func(n, b):
    a = [0] * n
    x = -1
    x = max(x, b[0] - 0)
    a[0] = b[0]
    for i in range(1, n):
        x = max(x, a[i - 1])
        a[i] = x + b[i]
    return a

if __name__ == '__main__':
    st = ''
    n = I()
    l = list(In())
    ans = func(n, l)
    print(*ans)