Farmer John is lining up his NN cows (2≤N≤1032≤N≤103), numbered 1…N1…N, for a photoshoot. FJ initially planned for the ii-th cow from the left to be the cow numbered ai**,ai, and wrote down the permutation a1,a2**,…,aNa1,a2,…,aN on a sheet of paper. Unfortunately, that paper was recently stolen by Farmer Nhoj!Luckily, it might still be possible for FJ to recover the permutation that he originally wrote down. Before the sheet was stolen, Bessie recorded the sequence b1**,b2**,…,bN−1b1,b2,…,bN−1 that satisfies bi**=ai**+ai**+1bi=ai+ai+1 for each 1≤i**<N.1≤i<N.

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

SCORING:

• Test cases 2-4 satisfy N≤**8.**N≤8.
• Test cases 5-10 satisfy no additional constraints.

INPUT FORMAT (file photo.in):

The first line of input contains a single integer N.N.The second line contains N−1N−1 space-separated integers b1**,b2**,…,bN−1**.**b1,b2,…,bN−1.

OUTPUT FORMAT (file photo.out):

A single line with NN space-separated integers a1**,a2**,…,aN**.**a1,a2,…,aN.

SAMPLE INPUT:

5
4 6 7 6

SAMPLE OUTPUT:

3 1 5 2 4

aa produces bb because 3+1=43+1=4, 1+5=61+5=6, 5+2=75+2=7, and 2+4=6.