Description

JOI-kun has $N$ go stones. The stones are numbered from $1$ to $N$. The color of each stone is an integer between $1$ and $10^9$, inclusive. In the beginning, the color of Stone $i$ ($1 \le i \le N$) is $A_i$.

From now, JOI-kun will perform $N$ operations. He will put the stones on the table in a line. The operation $i$ ($1 \le i \le N$) will be performed as follows:

1. JOI-kun will put Stone $i$ on the immediate right of Stone $i - 1$. However, when $i = 1$, JOI-kun will put Stone 1 on the table.
2. If there is a stone among Stones $1,2,\cdots,i-1$ whose current color is the same as Stone $i$, let $j$ be the maximum index of such stones, and JOI-kun will paint all of Stones $j+1,j+2,\cdots,i-1$ with the color $A_i$.

In order to confirm whether the operations are correctly performed, JOI-kun wants to know in advance the colors of the stones after all the operations are performed.

Given information of the go stones, write a program which determines the colors of the stones after the $N$ operations are performed.

Input Format

Read the following data from the standard input.

$N$
$A_1$
$A_2$
$\vdots$
$A_N$

Output Format

Write $N$ lines to the standard output. The $i$-th line ($1 \le i \le N$) should contain the color of Stone $i$ after the $N$ operations are performed.

6
1
2
1
2
3
2

1
1
1
2
2
2

10
1
1
2
2
1
2
2
1
1
2

1
1
1
1
1
1
1
1
1
2

Hint

Samples

Sample 1

The operations are performed as in the following table.

Finally, the colors of Stones 1, 2, 3, 4, 5, 6 will be 1, 1, 1, 2, 2, 2, respectively.

This sample input satisfies the constraints of Subtasks 1, 3.

Sample 2

This sample input satisfies the constraints of all the subtasks.

Constraints

• $1 \le N \le 2\times 10^5$.
• $1 \le A_i \le 10^9$ ($1 \le i \le N$).
• Given values are all integers.

Subtasks

1. (25 points) $N \le 2 000$.
2. (35 points) $A_i \le 2$ ($1 \le i \le N$).
3. (40 points) No additional constraints.