A13298. Maximums

Alicia has an array, $a_1, a_2, \ldots, a_n$ , of non-negative integers. For each $1 \leq i \leq n$ , she has found a non-negative integer $x_i = max(0, a_1, \ldots, a_{i-1})$ . 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, $b_1, b_2, \ldots, b_n$ : $b_i = a_i - x_i$ .

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 $b_1, b_2, \ldots, b_n$ and asks you to restore the values $a_1, a_2, \ldots, a_n$ . Can you help her solve the problem?

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

The next line contains $n$ integers, $b_1, b_2, \ldots, b_n$ ( $-10^9 \leq b_i \leq 10^9$ ).

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

Print $n$ integers, $a_1, a_2, \ldots, a_n$ ( $0 \leq a_i \leq 10^9$ ), 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.

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 $b = \{1000-0, 1000000000-1000, 0-1000000000\} = \{1000, 999999000, -1000000000\}$ .