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 ≤ i - a_i) or to the position i + a_i (if i + a_i ≤ 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).

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n), where a_i is the i-th element of a.

Output

Print n integers d_1, d_2, ..., 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.

Example

Input


10
4 5 7 6 7 5 4 4 6 4


Output


1 1 1 2 -1 1 1 3 1 1 
import java.io.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Arrays.*;

public class Solver {
    static int a[], n;
    static long ans[];
    static boolean vis[];

    static void dfs(int v) {
        vis[v] = true;
        if (v - a[v] >= 0) {
            if (((a[v - a[v]] ^ a[v]) & 1) == 1) ans[v] = 1;
            else if (!vis[v - a[v]]) dfs(v - a[v]);
            ans[v] = min(ans[v], ans[v - a[v]] + 1);
        }
        if (v + a[v] < n) {
            if (((a[v + a[v]] ^ a[v]) & 1) == 1) ans[v] = 1;
            else if (!vis[v + a[v]]) dfs(v + a[v]);
            ans[v] = min(ans[v], ans[v + a[v]] + 1);
        }
    }

    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        n = in.nextInt();
        a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = in.nextInt();
        }
        ans = new long[n];
        fill(ans, (long) 1e6);
        for (int i = 0; i < 100; i++) {
            vis = new boolean[n];
            for (int j = 0; j < n; j++) {
                dfs(j);
            }
        }
        for(int i = 0; i < n; i++) {
            out.print((ans[i] >= (long)1e6 ? -1 : ans[i]) + " ");
        }
        out.close();
    }
}

class FastScanner {
    BufferedReader br;
    StringTokenizer st;

    FastScanner(File f) throws FileNotFoundException {
        br = new BufferedReader(new FileReader(f));
    }

    FastScanner(InputStream is) {
        br = new BufferedReader(new InputStreamReader(is));
    }

    String next() throws IOException {
        while (st == null || !st.hasMoreTokens())
            st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    long nextLong() throws IOException {
        return Long.parseLong(next());
    }
}