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 bisect
import sys
input = sys.stdin.readline


def main():
    n = int(input())
    a = list(map(int, input().split()))
    b = list(map(int, input().split()))

    cnt = [0] * n
    for val in b:
        cnt[val] += 1

    all_set = sorted(set(b))
    n_all_set = len(all_set)

    nextL = [0] * n
    nextR = [0] * n
    for i in range(1, n_all_set):
        nextL[all_set[i]] = all_set[i-1]
    for i in range(n_all_set-1):
        nextR[all_set[i]] = all_set[i+1]

    nextR[all_set[-1]] = all_set[0]
    nextL[all_set[0]] = all_set[-1]

    res = []

    def opositeMod(x):
        return 0 if x == 0 else n-x

    for val in a:
        cand_pos = bisect.bisect_left(all_set, opositeMod(val))
        if cand_pos == n_all_set:
            cand_pos = 0

        cand_val = all_set[cand_pos]

        if cnt[cand_val] == 0:
            to_update = []
            current = nextR[cand_val]
            while cnt[current] == 0:
                to_update.append(current)
                current = nextR[current]
            for upd in to_update:
                nextR[upd] = current
                nextL[upd] = nextL[current]
            cand_val = current

        res.append((val+cand_val) % n)
        cnt[cand_val] -= 1
        if cnt[cand_val] == 0:
            nextL[nextR[cand_val]] = nextL[cand_val]
            nextR[nextL[cand_val]] = nextR[cand_val]

    print(*res)

if __name__ == '__main__':
    main()
