A question of Turaev about triple higher Milnor linking numbers of divide links

Abstract

The following question was pronounced, many years ago in Strasbourg, by Vladimir Turaev in the IRMA lecture room: Let $L \subset S^3$ be a link consisting of divide knots $K_1;K_2; \dots ;K_n$ given by divides $P_1; P_2; \dots ;P_n$. How to compute the Milnor higher linking numbers from the system of divides?

Also in the room was the question: Let $L \subset S^3$ be a link consisting of knots $K_1;K_2; \dots ;K_n$ given by Turaev shadows $S_1; S_2; \dots ;S_n$. How to compute the Milnor higher linking numbers from the system of shadows?

The present contribution answers the first question for the triple higher linking numbers.