Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

A. Duff and Weight Lifting

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputRecently, Duff has been practicing weight lifting. As a hard practice, Malek gave her a task. He gave her a sequence of weights. Weight of *i*-th of them is 2^{ w i} pounds. In each step, Duff can lift some of the remaining weights and throw them away. She does this until there's no more weight left. Malek asked her to minimize the number of steps.

Duff is a competitive programming fan. That's why in each step, she can only lift and throw away a sequence of weights 2^{ a 1}, ..., 2^{ a k} if and only if there exists a non-negative integer *x* such that 2^{ a 1} + 2^{ a 2} + ... + 2^{ a k} = 2^{ x}, i. e. the sum of those numbers is a power of two.

Duff is a competitive programming fan, but not a programmer. That's why she asked for your help. Help her minimize the number of steps.

Input

The first line of input contains integer *n* (1 ≤ *n* ≤ 10^{6}), the number of weights.

The second line contains *n* integers *w* _{1}, ..., *w* _{ n} separated by spaces (0 ≤ *w* _{ i} ≤ 10^{6} for each 1 ≤ *i* ≤ *n*), the powers of two forming the weights values.

Output

Print the minimum number of steps in a single line.

Examples

Input

5

1 1 2 3 3

Output

2

Input

4

0 1 2 3

Output

4

Note

In the first sample case: One optimal way would be to throw away the first three in the first step and the rest in the second step. Also, it's not possible to do it in one step because their sum is not a power of two.

In the second sample case: The only optimal way is to throw away one weight in each step. It's not possible to do it in less than 4 steps because there's no subset of weights with more than one weight and sum equal to a power of two.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/12/2020 02:19:16 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|