Marinada '21

[lang=hr] Ovaj puta nekako su došli do podužeg popisa informacija: \\ broj vojnika daje ostatak $1$ pri dijeljenju s $2$, ostatak $2$ pri dijeljenju s $3$, ..., ostatak $19$ pri dijeljenju s $20$. \\ Koliko znamenaka ima najmanji mogući broj vojnika koji zadovoljava navedene uvjete? [/lang] [lang=en] This time they somehow obtained a somewhat longer list of information about the soldiers: \\ it has a remainder of $1$ when divided by $2$, a remainder of $2$ when divided by $3$, ..., a remainder of $19$ when divided by $20$. \\ How many digits does the least possible number of soldiers which fulfills these requirements have? [/lang]