Competitions

# Photoshoot

Farmer John is lining up his n cows numbered 1 ... n for a photoshoot. FJ initially planned for the i-th cow from the left to be the cow numbered ai, and wrote down the permutation a1, a2,..., an on a sheet of paper. Unfortunately, that paper was recently stolen by Farmer Nhoj!

Luckily, it might still possible for FJ to recover the permutation that he originally wrote down. Before the sheet was stolen, Bessie recorded the sequence b1, b2, ...,bn−1 that satisfies bi = ai + ai+1 for each i (1i < n).

Based on Bessie's information, help FJ restore the "lexicographically minimum" permutation a that could have produced b. A permutation x is lexicographically smaller than a permutation y if for some j, xi = yi for all i < j and xj < yj (in other words, the two permutations are identical up to a certain point, at which x is smaller than y). It is guaranteed that at least one such a exists.

#### Input

The first line contains a single integer n (2n103). The second line contains n1 space-separated integers b1, b2, ...,bn−1.

#### Output

Print the lexicographically minimum permutation a1, a2,..., an.

#### Explanation

a produces b because 3 + 1 = 4, 1 + 5 = 6, 5 + 2 = 7 and 2 + 4 = 6.

Time limit 1 second
Memory limit 128 MiB
Input example #1
5
4 6 7 6

Output example #1
3 1 5 2 4

Source 2020 USACO January Bronze