XOR Inverse

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).

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.

inputFormat

outputFormat

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.

样例

9
10 7 9 10 7 5 5 3 5

4 14

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