Farthest Place

You are looking for a house to live in, choosing one of $N$ pieces of land. Three friends $A$, $B$, and $C$ have houses, and you want to find the place farthest from where these friends live.

The farthest place is the one that maximizes the distance to the nearest friend's house, measured from the house you choose.

For example, suppose the distances from a house at position $X$ to the houses of friends $A$, $B$, and $C$ are 3, 5, and 4, and the distances from a house at position $Y$ to the houses of friends $A$, $B$, and $C$ are 5, 7, and 2.

Then, of lands $X$ and $Y$, the one farther from the friends' houses is land $X$. The distance from $X$ to the nearest friend's house is 3, while from $Y$ it is 2.

Find the place farthest from the friends' houses.

The first line gives the number $N$ of candidate pieces of land.

The second line gives the positions where friends $A$, $B$, and $C$ live, separated by spaces. Each friend is guaranteed to live on one of the $N$ pieces of land. (They may live at the same position.)

The third line gives the number $M$ of roads connecting pieces of land.

From the next line through line $M + 3$, land $D$, land $E$, and the length $L$ of the road connecting land $D$ and land $E$ are given, separated by spaces. This road allows two-way travel.

Print the number of the land farthest from the friends' houses. If several lands are tied for farthest, print the land with the smallest number.

• $1 \le N \le 100,000$
• $N - 1 \le M \le 500,000$
• $1 \le A, B, C, D, E \le N$
• $1 \le L \le 10,000$
• $L$ is an integer
• The lands are numbered $1$ through $N$, one number each.
• Any two pieces of land are reachable from each other by road.