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## ACM_0118 - 3 NEAREST VILLAGES

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Assume the locations of any three villages are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3). The distance of the paths passing through any three villages are defined as

D = d12 + d23, where dij = |xi - xj| + |yi - yj| + |zi - zj|.

Determine the shortest path passing through the three closest villages.

#### Input

The first line specifies the number of villages, N (where 3 <= N <= 10,000). Each of the following N lines specifies the location (x, y, z) of each village (where -1000 <= x, y, z <= 1000).

#### Output

One line specifies the length of the shortest path passing through the three closest villages.

#### Examples

 № stdin stdout 1 9 0 0 1 0 0 2 0 0 3 0 0 4 0 0 6 0 0 8 0 0 7 0 0 9 0 0 10 2

 Added by: Հրանտ Հովհաննիսյան Date: 2014-02-02 Time limit: 2s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: ASM64 Resource: Thailand Central Group A 2013.B