Hello, everyone! Codeforces Round #631 will be held at Apr/03/2020 17:35 (Moscow time).

The problems are almost from me(dreamoon_love_AA), except one problem of which the idea is from drazil and developed by me. Also we want to thank 300iq for helping me prepare the round, isaf27, tmt514, rowdark, yp155136, wangyenjen, n_dao107 and zj713300 for testing this round, and MikeMirzayanov for Codeforces and Polygon.

This is my third time organizing a problemset for a Codeforces round (my previous rounds: Codeforces Round #292, Codeforces Round #320).

Good luck and have fun!

**UPD**: Below is a message for you from MikeMirzayanov:

*About two weeks ago, we completed the crowdfunding campaign dedicated to the 10th anniversary of Codeforces. Community help inspires and provides resources for the development and operation of the platform. Thanks! With this round, we want to say thank you to Denis aramis Shitov, for his significant contribution and support. It is valuable, important and very nice when people from the community lend a helping hand and congratulate. Thank you, Denis!*

**UPD2**: Also thanks to Shik for testing the round!

**UPD3**: Score distribution:

- Div2: 500 1000 1500 1750 2500
- Div1: 500 750 1500 2000 2500

**UPD4**: link to tutorial

**UPD5**:

I won't say sorry that the pretests are not strong. Because I don't think the pretests must be strong in every contest.

But I still want to give congratulations to the winners:

div1:

div2:

Among these winners, I want to especially congratulate Um_nik. I am quite excited when I see him solve all problems.

It's going to be a great round. Really Excited :)

But, be careful of test 1

This is not problem Generally, the test 1 is example in question and you will not get penalty even if you make a mistake on test 1.

Joke has gone above your head.

Yes but please everyone check their code answers on samples otherwise it will make the queue too long and reduces the quality of contest.

Indeed you are quite right

I see you know what meme is good

i wish god will save us from queue because there is lot of registration during quarantine.

But not all of them show up in contest.

ohh really?

Bitch,dreamoon is just rubbish and his contest is as rubbish as him.

Don't judge the quality of contests if you haven't taken them.

How many problems?

Usually, it is a 6 Problem and 2 Hour round.

I think there will be 5 problems for both division.

Thus this round must be relatively hard...unsatisfactory results ending up usually

But when I still studied in university, 5 problems round is more often than 6 problems. So I determine use 5 problems.

Wow! It's actually very exciting to see you back! And the problems are definitely gonna be extremely high-quality and hard to solve as well. Don't think it's wise to take part in such a round, cause oftentimes I failed to get my rating higher(sad face Anyway, wish the round a complete success!

Maybe it's just a round without div.1 A So it will be extremely hard.

definitely true LOL

So why I am downvoted? Just by predicting so accurately?

Let's see

U are really good manager[user:dreamoon_love_AA] ,Managing love and coding same time.

.

You mean for

eachdivision?What was wrong with the question — for both divisions there were 10 problems. :)

wow Setting Problem After such a long time

You have one of the most interesting rating graphs on codeforces!! dreamoon_love_AA

Please explain the trend!!

Yes you are right

Yes you are right that I am right

Yes you are definitely right that i am right that you are right.

.

I hope problem statements will also be short and sweet just like the announcement :)

Didnt invited sorry_dreamoon?

RIP English XD.

XD XD Even if that was not a joke, what's XD about it? XD XD

see from the side

RIP English

Care to elaborate??

Do you know there's a user called dreamoon_is_rubbish?

(S)He doesnt exists for me. Idk about others.

I think your name is not friendly to him/kk

Do you know there's a user called dizzy_izzy?

I wish the time could be earlier,I am not able to be there.o(╥﹏╥)o

RIP English XD.

lol your name -sister of contestfucker xdxd

yeah babyy, thass how i roll

Hope, everybody is going to enjoy the contest. :)

It will be interesting to see whether tourist can regain his throne in this contest!!!!

He can't. The contest is in ~35 hours.

edited!! :p :p

I didn't get you. What is the meaning of " The contest is in ~35 hours " ?

Nvm dude, you don't really want to spend your time on it

MiracleFaFa is hiding in his hole xD

Hope he didn't catch the virus.

it better be virus themed questions

I am excited for the contest , in this quarantine time it is just annoying and boring without cp contests and football matches .

can anyone suggest how to practice so that I am able to complete more than 2 problems in a contest?

there is no secret to it. just solve more tasks

what kind of tasks?

I am afraid bro I am not improving

I practiced with USACO or COCI problems. they give editorals.

Solve problems which are a little harder than your comfort zone. Like you can easily solve 1000 rating problems, then try to solve 1100-1200 rating problems. And don't spend more than 30 minutes on a problem if you think you are stuck see the tutorial, understand, and solve it.And of course

practice a lot.I am following this approach and it's helping me. happy coding.

Actually you can spend more than 30 minutes on a problem. You can spend as much time as you wish until you have some progress on it. Trust my words ;)

Problem setting tab shows you have arranged 3 contests before. Round 272,292 and 320. Then it should be your 4th contest. Why are you not considering round 292?

If you click the link of Round 272 provided in this blog, it opens up the page for Round 292.

That's another mysterious information.

I fix now...

Actually, I don't consider round 272 as const organized by me. It's the problemset of round 272 is not chosen by me. I just only provided the hardest problem to my friend.

Wow! This announcement is great! I think this round is going to be a great round.

dreamoon_love_AA here I come!!!

WHO ARE YOU? How dare you impersonate dreamoon?!/jk

Actually they're the same person

Actually we are not the same person

here I come too!

fuck you

Here we go again, one more

`I`

and`l`

scenario.So here is the difference -.-

I'm too surprised to see dreamoon_Iove_AA here!!!

It took me 10 minutes to figure out the difference in the usernames.

to understand the meme for none one piece fans

Auto comment: topic has been updated by dreamoon_love_AA (previous revision, new revision, compare).this is good ....

"Knowing Is Not Enough; We Must Apply. Wishing Is Not Enough; We Must Do.".......B)[user:hajer qandeel]tourist vs MiracleFaFa. Who will win ?

sorry_to_tourist

sorry_to_tourist

I think MiracleFaFa will win

World First MiracleFaFa!

// dlstxdy

what I think it would be exciting to watch as codejam would start in a day , tourist will try to get his throne back . lets see.who wins?

I guess you will have to wait a little longer. MiracleFaFa won't come out of his hole xD

Excited! Looking forward to your problems.

.

...

Who is Denis Aramis Shitov????

He is a friend of Codeforces. Please, re-read the blog post.

I am not begging for followers(friends) on codeforces.

Edit: I did not even edit my original comment uh.

Why are you begging for followers(friends) on codeforces?

Edit: Why would you even edit your original comment uh?

comment and its reply swapped XD

Feeling excited. Codeforces making this lockdown time easy to pass by holding the contests for programmers.

Let us see if this round can get 25000 registrations

All the best to everyone who will participate in this round. I hope to become a specialist after this contest.

Thank You Denis Aramis Shitov

tourist vs. MiracleFaFa It will be exiting!

after contest -> MiracleFaFa

Thank you mr. Denis Aramis Shitov

I hope I can do well in this round

%%%

I hope we can all achieve good results！

%%%

%%%

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is it rated?

yes it is rated

Of course,It will be rated.

Time is not good for me!

Thanks !!! We need competitions like this more and more .I wish everybody good luck.

Wow！It seems good！

I hope I'll get good grades in it.

Everybody hopes so.

Will it be a Mathforces Round?

I think it won't.

I hope its going to be an interesting round

Looking forward to seeing concise and crap free problem statements.

¯\_(ツ)_/¯

Thank you Mr.Denis Aramis Shitov.

umm..what we know so far is that there will be at least 2 problems

.

Read Announcement carefully before asking...

Trying to play MikeMirzayanov.

oh really? Priyank

thank you Denis aramis Shitov and to all other contributors.

Thanks, Danis and other contributors. Because of you, we have problems to solve for free.

Friendly reminder: watch out for FST.

What's the score for each problem?

.

fuck it

May God bless us from queue.... All the best guys!!!!!!!!!

Hope I will turn blue after this contest.

Hope this contest does not have long queues like the last rated contest

When the problem scroring will be posted?

I think , this contest will be very intersting

gl hf

thanks)) and to you

good luck for every one)

Why hasn't the score distribution been published yet?

hoping to do well in it and get some +ve rating . let's see how it goes .

Please post the score distribution of the problems.

I think will be 500-1000-1250-1500-2000

500-1000-1500-1750-2500

Auto comment: topic has been updated by dreamoon_love_AA (previous revision, new revision, compare).Is it rated ?

Unfortunately, it's not rated(

Really?

QAQ

QAQ? Is it really not rated?

Sarcasm

Malicious disinformation.

Enjoy the contest

site seems fast today

lets do well guys ..best of luck..

noExplanantionsForSamplesForces

orz

Did anyone else too missed the contest because they binge watched Money Heist ? :/ Guess I'm gonna give a virtual one now !

Lucky you...

Is this the second april fools round?

The authors likely spent some time writing the statement. Why do you think they can come up with a better explanation now in a shorter time? Besides that, it is much harder to understand your question than to understand the statement. $$$x$$$ is a number that is given to you in the input, what more do you want?

If they didn't say anything it would be better than this answer

No, I think it's an excellent answer.

It lets you know the

answer is written in the statement,the statement is clear(in the author's opinion) andyou do not need any more information. As opposed to "oops, we left this part out" and "yes indeed, it's unclear, we will edit". Not answering creates a lot of uncertainity. "No comment" is also a reasonable answer, but I think CF wants to be friendlier than that in easy problems.Not gonna lie you're right it's just a joke I don't why I can't understand it even though alot of people solved it

Lolwut, do you really think this is a reasonable question? This is definitely the appropriate answer given that thousands of people didn't have a problem with it.

Is this round bit hard!!!

OR only i feel so?

Pretty tought one :(

Great contest, I hate it.

I hate this contest! one of my worst performances so far could not even solve B!

Yeah, I also only solved 2. But the questions were really nice. I am waiting to see where I went stupid in my C and editorial for D.

how to find efficiently(better than O(k)) that all the number between 1 to k exist or not in a array of size k??

keep a count of the unique elements, as well as the maximum seen so far. Check if those are equal.

I used a set, if

`set.size() == max(set)`

then its a valid permutationand keep in mind to not add already added element

C made my heart go up and down.

Okay, Google

C for Cheater!

I thought problem B was harder than problem C but in fact more people solved problem B. The fact that I know number of solutions of B must be of the count 0, 1 and 2 actually makes the problem harder.

The worst contest i had seen!

How to solve Div.1 C?

Difficulty Ladder exploded?

Sorry, I read it as Div2 C. My bad.

I think greedily taking from the top layer that won't break your heap works (break your heap meaning having a 0 too high up).

Shitty greedy algorithm. Sort elements in decreasing order and erase if you can

yes the algorithm is shitty because your solution failed at test case 66 hahahahahha

You can check my submission, if you don't believe lessmeaning

Agreed

:)

i devoted more than 1 and half hout to problem B and ended up getting wrong answer . It just screwed up . But still enjoyed it.

I can't blame authors for my mistake but I think it wasn't obvious from the statement of problem div2C that queries must be performed in given order

What? I sorted the queries by length and wasted 1.5 hours and about 10 wrong submissions. I debugged on almost 50 test cases.

I spent about an hour trying to solve and I still didn't know this was the case until I read your comment

Glad to see I wasn't the only one. Took a long time to figure out, though I place all blame on me and none on the author. I have a bad habit of rushing the reading of the longer questions.

I think many have done this, and I feel coloring according to our own order is slightly more difficult question, I think I correctly solved that version, but the real question is very much easier and straightforward!

Anyone has an idea for pretest 6 of div2C?

It contains large values for each $$$l_i$$$. Using ints and adding them up will cause overflow, leading to WA.

omg why :'( you're right

It's not as crowded as recent contests but main page still can't load properly :(

i don't get it, seems like most struggled in this round , why would there be such a huge difference in div 2 rounds ?

was it a normal DIV2 contest?

The moment when you get runtime error in Div. 1 C in the last 5 mins....

How to solve Div1B?

SpoilerEach element has to have a higher bit on than the previous one, so try to build some DP with that

The main observation is that the numbers in your array must have strictly increasing MSBs (you can prove this by induction). From there, you can iteratively calculate the number of arrays with MSB at most $$$2^i$$$ for each $$$i$$$, and it's a slight modification once you have to do the MSB of $$$d$$$.

Sequence is ok iff msb($$$a_i$$$)<msb($$$a_{i+1}$$$). It can be calculated with simple dp.

An array that satisfies the given constraints mandates that the MSB of an element is greater than it's previous. No two elements can have the same MSB.

Let $$$A[i]$$$ be the number of elements that MSB at $$$i$$$th position that are less than $$$d$$$.

The answer is : $$$ ( (1+A[0])*(1+A[1]). . .*(1+A[32])) - 1 $$$.

We choose one number from each MSB bucket. We subtract the case where we choose 0 elements. We also take modulo $$$m$$$ at each multiplication step.

nice

Problem B(Div1) D(Div2):

You can't find this in OEIS

Me: 1 Hour trying to find it in OEIS

OEIS

This one is not the correct one.

orz ntf

VeryLongCodeWithoutBugForces

Anyone got an idea for Div2D ? Thanks :)

Main idea: We can find an array b for a given array a iff, for all i, a[i] has a larger leading bit than a[i-1].

Super balanced contest. Apart from that, ABD seem pretty nice, C could be but getting to right implementation can be tough and the constraint $$$2^20$$$ seems too tight.

After being unable to correctly implement my idea for a while, I realized it seems equivalent to a greedy which subsequently passed.

Apply

fon the topmost node such that after applyingfthere is no 0 in depth<= g. Very easy $$$O(nlogn)$$$ implementation for $$$n=2^h$$$.Hopefully correct.

Probably correct. I simulated that in a much more complicated way (and forgot that $$$G$$$ isn't $$$H-1$$$ because the sample doesn't contain that), but your example supports my point that a lot of this problem's difficulty is getting bogged down in ugly implementation.

Yeah, my code got extremely messy exactly due to $$$G$$$ not being $$$H-1$$$ as well. I didn't enjoy the problem either, but I guess it's still nice that a short correct code exists.

Solution 75417750 Contest submission 75411025

Proof: Consider the first time we make an operation not on the root, but on the path that making an operation on the root would modify. But making an operation on the root would be strictly better, as then all vertices would contain a smaller number. Also, applying that operation immediately after the last operation on the root instead of where it was originally done doesn't change anything.

Thus, we can first greedily apply operations to the root, then independently solve all branches of the path operating on the root would modify.

Actually my solution was super simple to code. I guess there are many ways to think about this problem, because mine solution is significantly different than one described by Enchom

Its code is here: https://ideone.com/1XiSlu

Personally I don't think that it's ok when D1B level problem becomes D1D level because you have to restore the answer.

Well, restoration of the answer in my solution is

where taken[i] means that I take number a[i] in the final answer :) (which I guess everybody needed to determine in order to get the first number right)

Or were you talking about Div1D and somehow messed up which comment you reply to :P?

EDIT: Ok, I think it is me who messed up xD. I kinda thought discussion under this post is about Div1C only, based on comments above. Don't mind me :<

Div1 D solution? Seems really hard. Seen a ton of similar problems but none of the usual techniques worked. Probably missing an observation of why some greedy part is correct.

Number of operations we have to make is

$$$ 1 + \max(\lceil\frac{\text{# of adjacent pairs of same character}}{2}\rceil, \max_{c \in \Sigma} (\text{# of adjacent pairs of character c})) $$$

As each operation decreases both quantities by at most one.

Greedy that works is always choosing the color with most adjacent pairs, then selecting some interval starting or ending with an adjacent pair of that color, and not both starting and ending with an adjacent pair of that color.

Implementing this greedy in $$$O(n^2)$$$ is easy, but I couldn't implement it fast enough to not TLE :(

find all occurrences 'aa' for all characters. Lets say if these type of occurrences is maximum for character a currently, then delete substrings of type aa....bb or bb....aa till it is possible to do so. This process ends when there are occurrences 'aa' for only one type of a character. Though the implementation was a bit too frustrating for me.

You can reduce it to the following problem: You are given a string and in every step you can remove two consecutive letters if they are different or an arbitrary single letter and you want to make it empty in the smallest possible number of steps.

Answer to that problem is max((length+1)/2, max frequency of a single letter)

Reduction from original problem is that for every pair of consecutive equal letter, you put that letter into that string in reduced problem. It can be easily seen that operations of removing beautiful string in original problem is allowed operation in that reduced problem, so they are equivalent.

Thanks. I made the reduction but for some reason the answer wasn't obvious to me. Quite disappointed that this is the solution to be honest.

And how to solve the problem after reduction? I found $$$\mathcal{O}(n^2)$$$ solution, but it shouldn't fit in TL if $$$n \approx 10^5$$$.

Oh well, that is a bit tedious task. In each step you determine the letter with biggest frequency (in O(26) cause I keep them explicitly) and we want to remove one of its occurences with some other one. Then you iterate over all other letters (another additive O(26), but beware, it's amortized!, because of reasons that will be clear later) and check whether there is any place where these two letter currently touch. In order to perform a single check you keep two-dimensional array (with size 26x26) of vectors of pairs that tell you where are currently neighbouring occurences of these pairs of letters. When you decide to remove some pair you need to remove 3 pairs and add 1. However removing is a bit inconvenient, so I do that lazily. That is, I do nothing in that moment of removing that pair and whenever I see some candidate for a neighbouring pair in one of these 26x26 vectors, I check whether this pair is still valid (that is, both letter are still alive) — if it is then I use it, if it isn't then I remove it. In order to know what new pairs of neighbouring letters are created I use my own bidirectional list. In order to restore indices in current string (based on global ones that I use everywhere) I use another bidirectional list for alive original positions and Fenwick tree.

I hope my code can be of some help: https://codeforces.com/contest/1329/submission/75411250

Oh, I got it, thanks!

Welcome

How to solve Div 2 D ?

I tried to do kind of cheating using Berlekamp-Massey algorithm to extrapolate the sequence manually but didn't work out.

Also if anyone got AC using BM algorithm please post your solution link.

How to solve div2 B? My submission gives TL on pretest 2.

maybe you used memset in each test case

yeah, is it wrong?

you have 10^4 test in each test case and you used memset on a array size 2e5 so it become n^2

Using memset for size n won't give tle as sum of n over all testcase always less than 200000. And all a_i is also less than n.

for clearing the arrays in independent testcases its better to use

fill function. this will take the time of size n given in the input . It doesn't lead to tle since sum of n over all testcases is <=2e5.I also used memset in each test case... 4 times (whoops? :)) )... and I passed all the pretests, so that shouldn't be the problem.

you just pass the pretests :))) but if you pass the protests that means memset is not the problem

If you use memset for size n then will never give tle but if you use memset for size 20000 in each case then you will surely get tle.

I used size 200000 each time. So... I guess a sweet TLE is awaiting me? :)): ...

I hope as 10^9 iteration is very large to complete in 2 seconds.

Nope, AC ¯\_(ツ)_/¯

You can use a multiset and a set

Create a multiset and a set that will be used as the prefix

Create another multiset and a set that will be used as the suffix

Iterate through the input array add the current value to the multiset prefix and the set prefix too

And remove the value from the multiset suffix and from the set suffix if the multiset doesn't contain the current value again

Now to check if a state is valid the multiset prefix size should be the same with the set prefix size and the largest element in the multiset prefix should be equal to the size of the multiset prefix check same for the suffix(multiset and set)

If valid add i and n — i — 1 to the result

CodeThanks a lot, I had a same algorithm but with memset, so I got TL(

you could use a vector and sort it then go throw it and check if each element is equal to its index+1

Traverse the array until you get 1st repeated element. When you get that break the array into two array at the point where you get 1st repeated value. Then simply check if two array is permutation or not.

Repeat the process starting from back.

In problem B, it was clearly written that two permutations are of non zero length, but this surely wasnt the case.

No, both permutaion length was >0

are you sure about it?

But they are of non zero length. a problem with the statement was the constraints saying both l1 and l2 <= n , not only their sums.

still , they are of non zero length , maybe you adding that to your code only fixed another bug.

Possibly, but adding an empty permutation somehow passed that testcase.

then unfortunately you probably will fail the main tests. this test is clearly wrong for you:

1

2

1 2

it should output: 0

while yours probably from what your saying will output:

1

2 0

1 2 1 2 answer for this should be 1 2 2 why it is wrong?

my bad , i am not sure why the comments here don't end lines like intended , fixed now.

And Poor me, couldn't figure out if l1=l2 they are considered as same permutation in an hour

I read div1A statement and for some reason, I thought "well, it's optimal to sort the values in decreasing order", but i never read that I wasn't allowed to change the order in which I use the array values. I realized about this when there were 10 minutes remaining of the contest. So sad to lose rating for that silly mistake. Goodbye div1, it was nice to meet you :(

If you're truly worthy you'll get it back soon :)

I did the same, and then after 30 minutes I realized that the queries should be done in order :/

Same here

How to do problem B div2?

First try checking valid sequence like all elements are 1 to n-1 , atleast there is one element with count 2. After that you can check till particular index if max=index and min=1 and sum=sum of permutation till index than insert in ans Same way for reverse array Take common elements

Thanks!

Hey can you tell me why this fails ? link

Thank you!

Because you are checking validity of permutation using sum of first x numbers. According to your code, both the below testcase will be considered valid permutation because their sum is equal to the sum of the first 5 elements. Sum({1 2 3 4 5}) = 15 [Valid] Sum({1 3 3 4 4}) = 15 [Not Valid]

I submit 3 wrong submissions while contest due to this, but finally Igot the point where I am stucking

Never noticed that the input is not a permutation in problem C, so sad......

What are the solutions for Div2C and Div2D?

How to solve Div2 C ?You are given m segments of different colors and you can slide these segments in a row of size n.

The maximum length we can get by spreading these segments is equal to the lengths of all the segments(i.e without any overlapping), let denote it by sum.

So if sum is less than n, it is not possible to cover the whole row.

Now if sum >= n we have to compress it to fit in the row size of n. We have to overlap some units of the cells(possibly zero) such that all the colors are visible.

The number of units cells to be overlapped is simply sum-n.

So start placing the segments from start of the row and after leaving sufficient units of cell place next segment(trying to overlap as much as possible but less than required length), and keep doing this for all the segments maintaining the required number of cells to be overlapped.

And if at any iteration the end of segment goes out of the window of size n, in that case answer is not possible.

My solution with above approach

thanks brother it really helped...

Does it take some time for problems to appear in the

Problem Setafter a contest is over? I think I finally found out what I was doing wrong in my Div2B code after an hour smh.1A(2C):hacker's paradise

Tried hacking O(M^2) solution on A (http://codeforces.com/contest/1329/submission/75404901) with ~2.5B operations. Passed in 1.45s (facepalm).

It looks like the optimizer changes

`while(ans[i] + a[i] - 1 < lst) ans[i]++;`

to`ans[i] = lst - a[i] + 1`

?No, since if it did, the code would run much faster than 1.45 seconds. It's just that the operations are very simple and the processor manages to execute them in time.

In problem c (div2) i tried following approach : first sort in descending order and then choose 'p' value such that first position of the current coloured segment does not coincides with first position of last coloured segment.my submission : link .can someone tell the mistake in approach ?

You can't change the order

I sorted back according to the indices so that order remains .

Colors are painted in the order of input, so you can't firstly paint one with largest $$$l_i$$$, then second largest etc.

Thanks , you are right . Because changing the order will cause some colour disappear when we reorder them to print . I removed sort lines from my code and it got accepted . submission

the order of coloring will remain as given.

How to solve Div1B/Div2D?

Use the observation that the required sequence is essentially a sequence of numbers such that the most significant bit is in increasing order. So, the max length of this sequence is at most 30.

Oh god, I got that observation before, but I just stopped thinking and doubting the problem statement which says it can't be found in OEIS, lol. I started spend too much time seeing similar pattern in OEIS and looking for how to code it. I should've just trusted the problem statement, what a nice lesson learned.

Or you know, don't use OEIS to solve problems.

Wow, that's a pretty bad contest if I've ever seen one. Speedforces for a lot of blues, who will now undeservingly be candidate masters.

Get your head out of your *ss mate

Well, I believe it gets balanced by upcoming contests.

Can anyone tell what could be the pretest 2 for DIV2 B...

Try your code for this input:

input1

10

1 2 3 4 5 4 3 2 1 6

I am getting

1

4 6

It failed on mine :( I got:

2

2 8

4 6

which is definitely wrong because I forgot checking if all numbers from 1-m exist. Took me an hour to notice it RIP

both l1 and l2 permutation of same number

1 1 1 Answer is 1 1 1

it was written in the problem statement that a[i]<n, hence this cannot be possible

Try this input to your code

Input1

8

1 1 1 7 7 1 1 1

WOW div2D/div1B is quite tricky. You can find the sequence on OEIS this sequence but only those few numbers in front of the sequence is right for this problem. So tricky/QAQ