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B. Welfare State

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere is a country with $$$n$$$ citizens. The $$$i$$$-th of them initially has $$$a_{i}$$$ money. The government strictly controls the wealth of its citizens. Whenever a citizen makes a purchase or earns some money, they must send a receipt to the social services mentioning the amount of money they currently have.

Sometimes the government makes payouts to the poor: all citizens who have strictly less money than $$$x$$$ are paid accordingly so that after the payout they have exactly $$$x$$$ money. In this case the citizens don't send a receipt.

You know the initial wealth of every citizen and the log of all events: receipts and payouts. Restore the amount of money each citizen has after all events.

Input

The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^{5}$$$) — the numer of citizens.

The next line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$0 \le a_{i} \le 10^{9}$$$) — the initial balances of citizens.

The next line contains a single integer $$$q$$$ ($$$1 \le q \le 2 \cdot 10^{5}$$$) — the number of events.

Each of the next $$$q$$$ lines contains a single event. The events are given in chronological order.

Each event is described as either 1 p x ($$$1 \le p \le n$$$, $$$0 \le x \le 10^{9}$$$), or 2 x ($$$0 \le x \le 10^{9}$$$). In the first case we have a receipt that the balance of the $$$p$$$-th person becomes equal to $$$x$$$. In the second case we have a payoff with parameter $$$x$$$.

Output

Print $$$n$$$ integers — the balances of all citizens after all events.

Examples

Input

4 1 2 3 4 3 2 3 1 2 2 2 1

Output

3 2 3 4

Input

5 3 50 2 1 10 3 1 2 0 2 8 1 3 20

Output

8 8 20 8 10

Note

In the first example the balances change as follows: 1 2 3 4 $$$\rightarrow$$$ 3 3 3 4 $$$\rightarrow$$$ 3 2 3 4 $$$\rightarrow$$$ 3 2 3 4

In the second example the balances change as follows: 3 50 2 1 10 $$$\rightarrow$$$ 3 0 2 1 10 $$$\rightarrow$$$ 8 8 8 8 10 $$$\rightarrow$$$ 8 8 20 8 10

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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