You are given an array a consisting of n non-negative integers. You have to choose a non-negative integer x and form a new array b of size n according to the following rule: for all i from 1 to n, b_i = a_i ⊕ x (⊕ denotes the operation [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR)).

An inversion in the b array is a pair of integers i and j such that 1 ≤ i < j ≤ n and b_i > b_j.

You should choose x in such a way that the number of inversions in b is minimized. If there are several options for x — output the smallest one.

Input

First line contains a single integer n (1 ≤ n ≤ 3 ⋅ 10^5) — the number of elements in a.

Second line contains n space-separated integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Output two integers: the minimum possible number of inversions in b, and the minimum possible value of x, which achieves those number of inversions.

Examples

Input


4
0 1 3 2


Output


1 0


Input


9
10 7 9 10 7 5 5 3 5


Output


4 14


Input


3
8 10 3


Output


0 8

Note

In the first sample it is optimal to leave the array as it is by choosing x = 0.

In the second sample the selection of x = 14 results in b: [4, 9, 7, 4, 9, 11, 11, 13, 11]. It has 4 inversions:

  * i = 2, j = 3; 
  * i = 2, j = 4; 
  * i = 3, j = 4; 
  * i = 8, j = 9. 



In the third sample the selection of x = 8 results in b: [0, 2, 11]. It has no inversions.
n = input()
a = [list(map(int, input().split()))]
ans = 0
x = 0
for w in range(31, -1, -1):
    w = 1<<w
    b = []
    sum_inv_one = 0
    sum_inv_zero = 0
    for aa in a:
        one = 0
        zero = 0
        inv_one = 0
        inv_zero = 0
        a1 = []
        a0 = []
        for i, ai in enumerate(aa):
            if ai & w:
                one += 1
                inv_one += zero
                a1.append(ai)
            else:
                zero += 1
                inv_zero += one
                a0.append(ai)
        sum_inv_one += inv_one
        sum_inv_zero += inv_zero
        if a1:
            b.append(a1)
        if a0:
            b.append(a0)
        # print(w, a0, a1)
    if sum_inv_zero > sum_inv_one:
        ans += sum_inv_one
        x |= w
    else:
        ans += sum_inv_zero
    a = b

print(ans, x)