CF1272E Nearest Opposite Parity

You 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).

The 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 $ .

Print $ 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.