You are given two arrays a and b, both of length n. All elements of both arrays are from 0 to n-1.

You can reorder elements of the array b (if you want, you may leave the order of elements as it is). After that, let array c be the array of length n, the i-th element of this array is c_i = (a_i + b_i) \% n, where x \% y is x modulo y.

Your task is to reorder elements of the array b to obtain the lexicographically minimum possible array c.

Array x of length n is lexicographically less than array y of length n, if there exists such i (1 ≤ i ≤ n), that x_i < y_i, and for any j (1 ≤ j < i) x_j = y_j.

Input

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

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i < n), where a_i is the i-th element of a.

The third line of the input contains n integers b_1, b_2, ..., b_n (0 ≤ b_i < n), where b_i is the i-th element of b.

Output

Print the lexicographically minimum possible array c. Recall that your task is to reorder elements of the array b and obtain the lexicographically minimum possible array c, where the i-th element of c is c_i = (a_i + b_i) \% n.

Examples

Input


4
0 1 2 1
3 2 1 1


Output


1 0 0 2 


Input


7
2 5 1 5 3 4 3
2 4 3 5 6 5 1


Output


0 0 0 1 0 2 4 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main2 {

    private FastScanner scanner = new FastScanner();

    public static void main(String[] args) {
        new Main2().solve();
    }

    private void solve() {

        int n = scanner.nextInt();

        int a[] = new int[n], b[] = new int[n];

        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }

        TreeMap<Integer, Integer> m = new TreeMap<>();
        for (int i = 0; i < n; i++) {
            b[i] = scanner.nextInt();
            m.put(b[i], m.getOrDefault(b[i], 0) + 1);
        }

        int c[] = new int[n];

        for (int i = 0; i < n; i++) {
            int need = n - a[i];

            Integer found = m.ceilingKey(need);
            if (found == null) {
                found = m.firstKey();
            }
            c[i] = (a[i] + found) % n;

            int ost = m.get(found) - 1;
            m.put(found, ost);
            if (ost == 0) {
                m.remove(found);
            }
        }

        for (int i = 0; i < n; i++) {
            System.out.print(c[i] + " ");
        }

    }

    long gcd(long a, long b) {
        if (b != 0) {
            return gcd(b, a % b);
        }
        return a;
    }

    class FastScanner {
        BufferedReader reader;
        StringTokenizer tokenizer;

        FastScanner() {
            reader = new BufferedReader(new InputStreamReader(System.in), 32768);
            tokenizer = null;
        }

        String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();

        }

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

        int[] nextA(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = scanner.nextInt();
            }
            return a;
        }

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

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}