Antarctic Exploration

Sanggeun owns the travel agency "Dreaming of Ice." The agency has bought $N$ islands near Antarctica and runs day trips there. The most popular animal among tourists is the emperor penguin, and it is easy to find on the islands.

The agency has grown more popular, to the point where moving tourists by boat is no longer efficient. Sanggeun plans to build bridges between the islands and move tourists by bus. He will manage the bridge-building process with a computer program.

The islands are numbered $1$ through $N$. At first there are no bridges, and the number of penguins living on each island is known. The number of penguins can change, but it is always between $0$ and $1000$ inclusive.

Sanggeun's program must handle three commands.

• bridge A B: build a bridge between islands $A$ and $B$. ($A$ and $B$ are different.) The bridge must be built only when $A$ and $B$ cannot be reached from each other using the bridges built so far. Print yes if the bridge must be built, and no if it is already possible to travel between them and no bridge is needed.
• penguins A X: a recount shows that island $A$ now has $X$ penguins. Print nothing.
• excursion A B: tourists take a route that starts at island $A$ and ends at island $B$. If $A$ can be reached from $B$, compute and print the total number of penguins on all islands along the route. (Include $A$ and $B$.) If the route is impossible, print impossible.

Write Sanggeun's program.

No further command is given before the answer to a bridge or excursion command is printed. Therefore, the standard output buffer must be flushed after printing.

The first line gives the number of islands $N$ ($1 \le N \le 30,000$).

The second line gives the number of penguins on each island.

The third line gives the number of commands $Q$ ($1 \le Q \le 300,000$).

The next $Q$ lines each contain one of the commands described in the problem.

Print a line each time a bridge or excursion command is given.