Farmer John has acquired a set of $N$ ($2 \le N \le 2,000$) touchy cows who are conveniently numbered 1..$N$. They really hate being too close to other cows. A lot.

FJ has recorded the integer $X_{i}$,$Y_{i}$ coordinates of every cow i ($1 \le X_{i} \le 100,000; 1 \le Y_{i} \le 100,000$).

Among all those cows, exactly two of them are closest together. FJ would like to spread them out a bit. Determine which two are closest together and print their cow id numbers (i) in numerical order.

By way of example, consider this field of cows (presented on a typewriter grid that has slightly different proportions than you might expect):

                    10 | . . . . . . . 3 . . . . .
                     9 | . 1 . . 2 . . . . . . . .
                     8 | . . . . . . . . . . . . .
                     7 | . . . . . . . . . . 4 . .
                     6 | . . . . . . 9 . . . . . .
                     5 | . 8 . . . . . . . . . . .
                     4 | . . . . . 7 . . . . . . .
                     3 | . . . . . . . . . 5 . . .
                     2 | . . . . . . . . . . . . .
                     1 | . . . . 6 . . . . . . . .
                     0 ---------------------------
                                           1 1 1 1
                       0 1 2 3 4 5 6 7 8 9 0 1 2 3

Quick visual inspection shows that cows 7 and 9 are closest together (the distance separating them is $\mathrm{sqrt}(1*1+2*2) = \mathrm{sqrt}(5)$, so the output would be '7 9' on a single line (without quotes, of course).

Input

• Line 1: A single integer: $N$
• Lines 2..$N$+1: Line i contains the coordinates of cow i expressed as two space-separated integers: $X_{i}$ and $Y_{i}$

Output

• Line 1: The two numerical IDs of the closest pair of cows (sorted)

Examples

Input 1

9
2 9
5 9
8 10
11 7
10 3
5 1
6 4
2 5
7 6

Output 1

7 9

As in the example.

Problem credits: Rob Kolstad, 2009