2000019202

People in Kocourkov pay by coins named groschen. Their coins are worth $1$, $5$ or $7$ groschen. Martin and Petr, who live in Kocourkov, emptied their saving boxes and started counting their saved coins. They found out that Petr had $6$ pieces of each type of a coin more than Martin, who had $40$ coins in total. They were surprised to find out that Martin has the same number of $1$-groschen and $7$-groschen coins in total as Petr has of $5$-groschen ones. Petr was proud to have $78$ groschen more than Martin, who was only $2$ short of having $200$ groschen. How many coins did Martin have?