E. Nearest Opposite Paritytime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a consisting of n integers. In one move, you can jump from the position i to the position i - a_i (if 1 \le i - a_i) or to the position i + a_i (if i + a_i \le n).For each position i from 1 to n you want to know the minimum the number of moves required to reach any position j such that a_j has the opposite parity from a_i (i.e. if a_i is odd then a_j has to be even and vice versa).InputThe first line of the input contains one integer n (1 \le n \le 2 \cdot 10^5) — the number of elements in a.The second line of the input contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le n), where a_i is the i-th element of a.OutputPrint n integers d_1, d_2, \dots, d_n, where d_i is the minimum the number of moves required to reach any position j such that a_j has the opposite parity from a_i (i.e. if a_i is odd then a_j has to be even and vice versa) or -1 if it is impossible to reach such a position.ExampleInput
10
4 5 7 6 7 5 4 4 6 4
Output
1 1 1 2 -1 1 1 3 1 1 

10
4 5 7 6 7 5 4 4 6 4

1 1 1 2 -1 1 1 3 1 1  
['dfs and similar', 'graphs', 'shortest paths', '*1900']