The Fair Nut and Rectangles

The Fair Nut got stacked in planar world. He should solve this task to get out.

You are given n rectangles with vertexes in (0, 0), (x_i, 0), (x_i, y_i), (0, y_i). For each rectangle, you are also given a number a_i. Choose some of them that the area of union minus sum of a_i of the chosen ones is maximum.

It is guaranteed that there are no nested rectangles.

Nut has no idea how to find the answer, so he asked for your help.

Input

The first line contains one integer n (1 ≤ n ≤ 10^6) — the number of rectangles.

Each of the next n lines contains three integers x_i, y_i and a_i (1 ≤ x_i, y_i ≤ 10^9, 0 ≤ a_i ≤ x_i ⋅ y_i).

It is guaranteed that there are no nested rectangles.

Output

In a single line print the answer to the problem — the maximum value which you can achieve.

Examples

Input

3 4 4 8 1 5 0 5 2 10

Output

9

Input

4 6 2 4 1 6 2 2 4 3 5 3 8

Output

10

Note

In the first example, the right answer can be achieved by choosing the first and the second rectangles.

In the second example, the right answer can also be achieved by choosing the first and the second rectangles.

inputFormat

Input

The first line contains one integer n (1 ≤ n ≤ 10^6) — the number of rectangles.

Each of the next n lines contains three integers x_i, y_i and a_i (1 ≤ x_i, y_i ≤ 10^9, 0 ≤ a_i ≤ x_i ⋅ y_i).

It is guaranteed that there are no nested rectangles.

outputFormat

Output

In a single line print the answer to the problem — the maximum value which you can achieve.

Examples

Input

3 4 4 8 1 5 0 5 2 10

Output

9

Input

4 6 2 4 1 6 2 2 4 3 5 3 8

Output

10

Note

In the first example, the right answer can be achieved by choosing the first and the second rectangles.

In the second example, the right answer can also be achieved by choosing the first and the second rectangles.

样例

4
6 2 4
1 6 2
2 4 3
5 3 8

10

</p>