Given $n$ points $P(x,y)$ in a plane, find:

$$\min_{i \ne j} |P_i - P_j|$$

Input

The first line of input contains one integer $n$.

The next $n$ lines each contain two integers $x, y$.

Output

Output a single real number.

Examples

Input 1

5
4 8
5 2
3 7
6 10
1 3

Output 1

1.4142135623730950488016887242097

Input 2

6
24 58
39 67
18 57
92 83
75 10
5 7

Output 2

6.0827625302982196889996842452021

Input 3

10
123 534
823 759
127 854
359 583
824 758
756 827
347 582
976 845
473 375
675 347

Output 3

1.4142135623730950488016887242097

Input 4

50
237 24
326 153
234 51
388 349
467 269
486 19
64 105
129 205
66 285
463 235
296 78
323 407
137 207
401 339
57 91
157 6
237 81
452 463
431 420
230 134
100 92
228 351
443 415
466 293
88 86
154 455
435 470
311 312
185 397
408 177
271 26
270 333
362 59
228 74
281 213
441 16
49 263
176 117
273 76
197 294
466 214
491 447
18 343
288 295
427 137
177 167
191 201
180 289
384 92
130 164

Output 4

8.2462112512353210996428197119482

Subtasks

Your answer is considered correct if and only if the error does not exceed $10^{-6}$.

For all data, $2 \leq n \leq 2 \times 10^6$, $1 \leq x_i, y_i \leq 10^{9}$.

Subtask 1 (15 points): $n \leq 3000$

Subtask 2 (25 points): $n \leq 50000$

Subtask 3 (15 points): $n \leq 5 \times 10^5$

Subtask 4 (20 points): $n \leq 10^6$

Subtask 5 (25 points): $n \leq 2 \times 10^6$