B. Maximumstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAlicia 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?InputThe 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.OutputPrint 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.ExamplesInput
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 NoteThe 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\}.
5
0 1 1 -2 1

0 1 2 0 3 
['implementation', 'math', '*900']