No tag edit access

E. LIS of Sequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe next "Data Structures and Algorithms" lesson will be about Longest Increasing Subsequence (LIS for short) of a sequence. For better understanding, Nam decided to learn it a few days before the lesson.

Nam created a sequence *a* consisting of *n* (1 ≤ *n* ≤ 10^{5}) elements *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{5}). A subsequence *a*_{i1}, *a*_{i2}, ..., *a*_{ik} where 1 ≤ *i*_{1} < *i*_{2} < ... < *i*_{k} ≤ *n* is called increasing if *a*_{i1} < *a*_{i2} < *a*_{i3} < ... < *a*_{ik}. An increasing subsequence is called longest if it has maximum length among all increasing subsequences.

Nam realizes that a sequence may have several longest increasing subsequences. Hence, he divides all indexes *i* (1 ≤ *i* ≤ *n*), into three groups:

- group of all
*i*such that*a*_{i}belongs to no longest increasing subsequences. - group of all
*i*such that*a*_{i}belongs to at least one but not every longest increasing subsequence. - group of all
*i*such that*a*_{i}belongs to every longest increasing subsequence.

Since the number of longest increasing subsequences of *a* may be very large, categorizing process is very difficult. Your task is to help him finish this job.

Input

The first line contains the single integer *n* (1 ≤ *n* ≤ 10^{5}) denoting the number of elements of sequence *a*.

The second line contains *n* space-separated integers *a*_{1}, *a*_{2}, ..., *a*_{n} (1 ≤ *a*_{i} ≤ 10^{5}).

Output

Print a string consisting of *n* characters. *i*-th character should be '1', '2' or '3' depending on which group among listed above index *i* belongs to.

Examples

Input

1

4

Output

3

Input

4

1 3 2 5

Output

3223

Input

4

1 5 2 3

Output

3133

Note

In the second sample, sequence *a* consists of 4 elements: {*a*_{1}, *a*_{2}, *a*_{3}, *a*_{4}} = {1, 3, 2, 5}. Sequence *a* has exactly 2 longest increasing subsequences of length 3, they are {*a*_{1}, *a*_{2}, *a*_{4}} = {1, 3, 5} and {*a*_{1}, *a*_{3}, *a*_{4}} = {1, 2, 5}.

In the third sample, sequence *a* consists of 4 elements: {*a*_{1}, *a*_{2}, *a*_{3}, *a*_{4}} = {1, 5, 2, 3}. Sequence *a* have exactly 1 longest increasing subsequence of length 3, that is {*a*_{1}, *a*_{3}, *a*_{4}} = {1, 2, 3}.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 08:11:52 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|