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 sys
input = sys.stdin.readline

def make_tree(n):
    i = 2
    while True:
        if i >= n * 2:
            tree = [inf] * i
            break
        else:
            i *= 2
    return tree

def initialization(a):
    l = len(tree) // 2
    for i in range(l, l + len(a)):
        tree[i] = a[i - l]
    for i in range(l - 1, 0, -1):
        tree[i] = min(tree[2 * i], tree[2 * i + 1])
    return

def update(i, x):
    i += len(tree) // 2
    tree[i] = x
    i //= 2
    while True:
        if i == 0:
            break
        tree[i] = min(tree[2 * i], tree[2 * i + 1])
        i //= 2
    return

def find(s, t):
    s += len(tree) // 2
    t += len(tree) // 2
    ans = inf
    while True:
        if s > t:
            break
        if s % 2 == 0:
            s //= 2
        else:
            ans = min(ans, tree[s])
            s = (s + 1) // 2
        if t % 2 == 1:
            t //= 2
        else:
            ans = min(ans, tree[t])
            t = (t - 1) // 2
    return ans

n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
inf = 114514810
tree = make_tree(2 * n + 1)
cnt = [0] * n
x = [inf] * (2 * n)
for i in b:
    cnt[i] += 1
    x[i] = i
    x[i + n] = i + n
initialization(x)
c = []
for i in a:
    l = n - i
    r = l + n - 1
    m = find(l, r) % n
    c.append((i + m) % n)
    cnt[m] -= 1
    if not cnt[m]:
        update(m, inf)
        update(m + n, inf)
print(*c)