Marinada '23

[lang = hr] Zadan je potpun graf od $1001$ čvora. Bridovi su mu obojani u $n$ boja. Za svaku boju vrijedi: kada bismo gledali samo bridove odabrane boje, graf ne bi bio povezan. Za svaki par boja vrijedi: kada bismo gledali samo bridove koji su obojani u jednu od odabranih boja boje, graf bi bio povezan. \\Kolika je najmanja vrijednost koju $n$ može poprimiti? [/lang] [lang = en] A complete graph of $1001$ nodes is given. Its edges are painted in $n$ colors. It is true for every color: if we looked only at the edges of the selected color, the graph would not be connected. For every pair of colors it is true: if we were to look only at the edges that are colored in one of the selected colors, the graph would be connected. \\What is the smallest value that $n$ can take? [/lang]