BNW Deity Tier List

Why is England so good? They are just a vanilla civ which doesn't get any benefit (oh well, faster work boats and triremes...) until longbowmen and spies show up. Are they really redeemed by the excessive power of SotLs?

The longbow has excessive power too. It's the main reason why England is so good - no matter where they go, land or sea, they have a great UU that shows up for it in the early midgame.
 
Why are the celts so high? They're a bottom tier civ imo

They're one of the very few civs that can reliably found a religion on Deity, they have a very good UB (yeah it's no pyramid but +3 happiness is pretty good) and their UA is decent and synergizes nicely with their religious bias.
 
I'm not gonna advocate an immediate drop or anything, but I'm kind of curious, is Arabia really still a God Tier civ? I mean, they're good, sure. Bazaar is one of the best UB's in the game...but their UA has, IMO, been reduced in usefulness compared to the gold bonus they had pre-BNW, and their UU is still strong, sure, but do you really want to use it given that to maximize their other bonuses you really rather not go to war?
Despite having that Desert bias, I don't find it easy to actually grab Desert Folklore due to the ridiculous bonuses of the AI. This is a big one to me as well.
Basically, I'm just not sure they're on the level of the silly bonuses of the Maya/Korea/Babylon/Poland group. I think they're more on the level of China as a civ that can definitely play with the big boys but does prefer a specific kind of map for that, and in all other cases as a very good and powerful but just not god tier civ.
Just food for discussion, I guess.
 
Why are the celts so high? They're a bottom tier civ imo

Read the thread. There's been a ton of discussion on them. I had them in middle tier originally, but a bunch of people got mad and moved them up. Their UU is one of the most useful ancient/classical UUs in the game for barb-hunting, because you actually get something out of it, and you can send them to fight barbs 1v1 with no backup. Ironic, since in G&K, their UU were one of the best for a totally different reason (I mean, you can still do this on small continents if your start is 2/3-civ iso enough).

They are still usually first pantheon, and they're able to get a religion consistently (and usually first, if you're using the UUs right) without needing to going down Piety or getting temples. It does screw with their city placements, but they can go wide(r) because of a +3 happiness per city bonus (in a building that you'll need to build whether going for CV or not; in CV, it's necessary before museums, in non-CV, you still want something to do with those musicians you get for working culture slots).

It's a pretty much guaranteed decent start, and they can really make Liberty work well on Deity. And of course, Tradition always works (+12 happiness in mid-game to bridge the gap to ideologies is nothing to sneeze at; not to mention being able to have a religion going tradition, so you get to pick things like swords to ploughshares). They're Ethiopia, without the military bonus, and with a happiness bonus. Now, they're not as good as Ethiopia, but the difference is not stark.

The only civ with a faith bonus that is not in the top two tiers is Indonesia. And that's only because it comes too late to help found a religion (so you're not guaranteed a religion on Deity).
 
I'm not gonna advocate an immediate drop or anything, but I'm kind of curious, is Arabia really still a God Tier civ? I mean, they're good, sure. Bazaar is one of the best UB's in the game...but their UA has, IMO, been reduced in usefulness compared to the gold bonus they had pre-BNW, and their UU is still strong, sure, but do you really want to use it given that to maximize their other bonuses you really rather not go to war?
Despite having that Desert bias, I don't find it easy to actually grab Desert Folklore due to the ridiculous bonuses of the AI. This is a big one to me as well.
Basically, I'm just not sure they're on the level of the silly bonuses of the Maya/Korea/Babylon/Poland group. I think they're more on the level of China as a civ that can definitely play with the big boys but does prefer a specific kind of map for that, and in all other cases as a very good and powerful but just not god tier civ.
Just food for discussion, I guess.


Even without their own religion, arabia is still generating enough fpt to be effective later(GPS purchases) and can purchase faith stuff from other religions. Another thing about their start bias is that if u start in desert your opponets aren't very likely to spawn on desert and pick folklore.

Bazaar - generates lump sums for upgrades,rush-buy stuf, etc etc. Really crucial on deity.

UA is kind of weaker in BNW but the extra range helps have more than one trade partner in the early game.

Keshiks - I don't know about you but i consider them in the top 3 units on Pangea map depending ot the situation.

To sum up - Their bonuses makes them strong civ in the early,mid and late game(double oil - spam planes,tanks). That is why they are top tier. Synergy is everything.
 
Indeed, camel archers. Very much the same :D

Well, I noticed on other thread, one was wondering why Rome is in the Upper Tier. I actually agree with him but maybe didn't notice at the begining. Reading the thread further (this thread), I saw that there was one short discussion about Rome and then OP wrote he wants to discuss this, so here i am writting

So are Rome really that good civ to be considered Uppet Tier. In the same tier as Austria and Ethiopia? Yes, their UA is flexible and stuff. But their UUs are not very good. I loved playing Rome in Vanilla with the march style where you just build billions ballistas and legions, walk in a straight line and smash everything under the armored foots of the legions sieging the AIs caps, taking them in 2 turns in the early game (building roads for your ballistas at same time). They are suited best for playing wide and then switch to playing tall using your UA and by doing this getting not only 1 or 2 great cities but getting 4+ great cities. I cannot think of any other way playing them at their best.

First you need so much iron to makes legions+ballistas push to work, and if you are not massively using them for that strat Rome is played the same way as America, Brazil and Russia are played at this turn-time ( also these other civs have other UUs coming later in to an account). Second, we are speaking about deity. During the era Rome is the strongest, AIs have ridiculous advantage and most of the time they are on the march against you and both of Rome's UUs suck at being sieged and marched upon. Legion is not really that better of its replacement.

I think you should really consider lowering them by one ( maybe putting an ^ to them, since they are generally better on Pangea, but not really sure about that).Rome is actually crappy on Archipellago when goind wide is a problem, Optics far a way from their best tech path( it is very hard to get UUs and Optics on time so your attack actually do something), roads don't really needed. I didn't yet played them in BNW but i don't think there is a big change at their playstyle since vanilla and that is 2 expansions.
 
So are Rome really that good civ to be considered Uppet Tier. In the same tier as Austria and Ethiopia? Yes, their UA is flexible and stuff. But their UUs are not very good. I loved playing Rome in Vanilla with the march style where you just build billions ballistas and legions, walk in a straight line and smash everything under the armored foots of the legions sieging the AIs caps, taking them in 2 turns in the early game (building roads for your ballistas at same time). They are suited best for playing wide and then switch to playing tall using your UA and by doing this getting not only 1 or 2 great cities but getting 4+ great cities. I cannot think of any other way playing them at their best.

I didn't yet played them in BNW but i don't think there is a big change at their playstyle since vanilla and that is 2 expansions.

Play a game and see. Don't attack anyone. Don't build more than a couple of legion (like, literally 2, and don't upgrade them until post-railroads). Ignore the ballista. Go liberty and found 6-8 cities by mid-game (they don't have to all be great cities, just make sure your happiness is keeping up). Use food/hammer routes liberally in mid-game. Gold-buy every science building in the capital (and anything else you want in all your cities fast). Or, even if you go tradition, Rome's UA will be valuable enough to justify it's spot. Just go by how smooth things feel at the end. Unless you are very meticulous about the timing of each tech/building, you won't notice anything. You'll just think things are going well.... always. But the math shows Rome's UA's power. See below:

The problem with BNW is that hammers have become scarce in relation to what must be built. In Vanilla, you could build everything in a tall empire which pursuing the most science-route using hammers in a Tradition 4-city build. In G&K, you start to run into some issues where your science is outpacing your production. But, that's fine, there're some buildings you don't need anyway. In BNW, there are a ton of buildings, almost all of which are useful and have compounded values (so, you want to get them asap). For most BNW civs, this means you'll be using gold to buy some buildings. But, gold is SUPER inefficient. To give you an idea of how awful gold-buying is.... Universities cost 160 hammers, or 660 gold. That's more than 4x the amount of gold!!!!! Keep in mind that to generate gold from tiles, it's usually a 1:1 tradeoff. This is why the AI in "default" city management settings always prioritizes gold dead last. Gold is both the hardest to get (especially in the early game), and the most worthless thing to use. Only at the very end-game, is gold so plentiful that you'll consider a 4:1 tradeoff to be fair value (mostly because you have no idea where else to spend it). Once you commit to "I don't run out of useful things to build until the very end of the game", Rome's UA becomes a direct 4:1 savings versus a gold bonus. Even better, Rome can just generate more value by plopping down another city, whereas most other UAs are locked to a set value (Portugal to # of trade routes; Greece to # of city states).

Anyway, when you follow the math, ANYTHING in BNW that saves hammers early/mid-game, is ridiculously important, and even more important on deity because you're teching at a faster rate. Rome's UA (4:1 important) is less impressive if you have 400 turns to hit the end of the tech tree, versus 250/300 turns.

Rome doesn't just save hammers, it saves an insane amount of hammers. Consider a comparison with Greece. Greece saves 50% of CS-directed gold. And, even in non-Greece games, you DO run out of CSes that need gold. It's not really a never-ending pit. Greece is a good comparison for value because it is also a "savings" type UA (whereas, with a pure gold bonus like Portugal, the flexibility has a certain value). In this case, Rome's 25% savings is actually twice as good as Greece's 50% savings, due to the natural 4:1 conversion rate... for all cities you run out of stuff to build (in a 4-city tradition, this means it's something like 150% the value of Greece's UA, not actually twice). In reality, even with Rome's hammer discount, you won't be able to build everything. And the discount gets really ridiculous when you have 6-8 cities, especially when obtained through peaceful spread. (Of course, conquest will ultimately generate more bonuses from the sheer number of cities you'll take and use, but it's less good on a per-city calculation).

Side note:

This is also why everything that saves or gives hammers is extra extra valuable (along with food, but that's more obvious), and everything that saves gold is not worth as much as it seems. This is not a "Civilization V" thing, this only happened in BNW. Before, in G&K and especially Vanilla, hammers were only extra valuable if you need to build units, because otherwise, you could more or less build everything you wanted. In BNW, your 4th city will be lucky to have generated half the number of hammers it needs to build everything you want. So, everything hammer-related got much better in BNW (to the degree of hammers saved/granted), including anything that allows you to trade off food on tiles. Direct Hammers: Poland, Egypt, Rome, Persia, Russia, Germany, Huns, Carthage, Iroquois. Food-tradeoff hammers: Inca, Siam, Netherlands, Aztec.

The low-tiered civs on this list have difficult to utilize hammers (for example, Iroquois may actually lose hammers in certain cities and during certain eras; Huns/Carthage gain/save very few hammers; Germany's hammer bonus doesn't really kick in until mid-late game, and it has a significant gold-opportunity cost). Being forced to create units also essentially raises the total hammer cost for your strategy, so aggressive civs need more hammers to begin with, and some of these UAs merely offset the need, by however much.
 
I am thinking about how right you are. Romes UA definetely is way more profitable in the BNW expansion. I don't have the time now (it is 3am here) to play a whole rome wide and tall game but I can see their benefits in gold saving and more importantly hammer saving. But I have one other thing that is in my mind now. How many times do you really get more than 4 cities ( and I am talking about cities that can grow to 15-18 pop, actually be useful of anything but building units, don't hurt your happiness pool) on Deity without any other Civ looking at you being agressively expansive. If we look at the map setting since this is not a Pangea-only list, Rome won't be able to expand to 6+ cities in 90% of the times on Archipelago maps. Another issue is the fact that even if you build these 6-8 efficient cities, I just can't see how you are not bordering someone (On Pangea especially). Not to mention that in Continents you will need to fight for that land. With that non-agressive playstyle, the chances of getting that kind of start seems very odd to me.

Well I definetely agree with you that your satelitte cities don't even need to be in great spots besides for growth but I now think that Rome is really hard to decide if it is actually bad, mediocre or good Civ. I believe that the start of the game is really what decides the game pre-200T and if you want to settle that expansively you can not play peaceful game and just build buildings for life. It comes to my mind, that if that kind of problem accure, your outter cities can build the units you need while cap is focused on production of the buildings and the cities can catch up easily.

With all that being said, I consider Rome a better Civ than before but are you sure they really deserve the place next to Ethiopia and Austria. Also in the tier description, you pointed that for that tier the Civ has guaranteed start( the other two things are present to the Rome's set of abilities). Imagine if you get a crappy capital with not enough hammers for the early-to-mid game and you can't snowball your hammers into being unstoppable production force. Game over.

Thank you for the nice and long replies. You really explain the math and mechanics about evrything. WoW, sorry for the typos, getting really tired, not the best time for a clear thought (misspelled Austria with Australia...)
 
Rome is one of those that plays smoothly but doesn't have "stark" bonuses which is why people underappreciate it. The UA is barely noticeable, but in the background, it works wonders. You don't even need alot of cities. I once had got crammed out of space and only managed 3 cities despite going liberty. The cities just developed smoothly and I had spare hammers for legions and cbs to smash a nearby civ for a well developed capital full of wonders. You don't need to go full domination. Once you have established a good base of 6 or so cities (built or conquered), just let the UA work its magic and you can pursue any victory you want. There's absolutely no need for Rome to get more cities. Whenever people talk about how Rome need to go wide, I just don't understand why. If you cant use a UA to its fullest potential doesnt mean that its a bad UA. For every four buildings you build, you can get one for free. Or you can substitute the free building for a free unit so you can go take a couple of cities from your neighbours if land is so scarce. Tradition only give you two free buildings throughout the game but Rome you can get about 2 free buildings every era.
 
The extra hammers are really noticeable when you're building your Libraries. I remember the first time I went Liberty with Rome and just thought to myself, dear God, I can hard build all of these without delaying the National College.
 
Thanks!

But I have one other thing that is in my mind now. How many times do you really get more than 4 cities ( and I am talking about cities that can grow to 15-18 pop, actually be useful of anything but building units, don't hurt your happiness pool) on Deity without any other Civ looking at you being agressively expansive. If we look at the map setting since this is not a Pangea-only list, Rome won't be able to expand to 6+ cities in 90% of the times on Archipelago maps. Another issue is the fact that even if you build these 6-8 efficient cities, I just can't see how you are not bordering someone (On Pangea especially). Not to mention that in Continents you will need to fight for that land. With that non-agressive playstyle, the chances of getting that kind of start seems very odd to me.

If you want to, it's not that hard on fractal/continents to get 6-8 cities. The key is to fence off an area and fill it in later. So, pretend the map is a square, all you have to do is cut off the angle with ~3 cities, and the AI won't expand through your cities until late-mid game, by which point should have filled in the cities already. I've never played Rome on a water-heavy map before, only Fractal/Continents/Pangaea. This list is for water/land balanced maps in any case. You really can't get 6 cities on Archipelago going Liberty? I haven't played Archipelago on Deity yet, but I know on large islands going wide is not a problem.

Remember, your cities really don't all need good land. In 4-city tradition, you need your cities to grow well or you won't have enough pop to keep up. In 6/8 city liberty, you're going to end up with more pop than tradition anyway, not to mention more specialist slots to take advantage of Rationalism. It gets exponentially harder to grow a city. But for cities to be ~20 pop, they all catch up pretty quick after they get a hospital. I'm satisfied with a city if it has 4 "things" within the limits I want to work, and 8 other workable tiles (non-tundra/desert/snow/water). That's only a ring and a half worth of workable tiles. Since you're building almost all buildings, you'll have plenty of specialist slots to put your extra pop (and they'll all generate science).

Any city that can grow to a pop of 6 will pay off it's science penalty with Rationalism. Math (assumption 1k science per turn): With 6 pop and library/university/school (3 farms, 3 specialists = (27 base science +33% + 17%) x 110% = 44 science, which is the per-city science needed for a city to pay for itself when researching final technologies, such as Internet). At 10 pop, you're definitely in the clear. This is what I mean by you don't really need good land to found more cities, just don't run out happiness that you can't grow your key science-cities. Happiness permitting, even if you are going for sub-250 win times, you can found a city on turn 150 and it will certainly cut down your spaceship turn time with 0 gold investment (the city will actually generate more gold for you). It will slow down policy acquisition though, and that breakpoint depends on how many cities you already have, and whether you have liberty. But, suffice to say it will be difficult to make up for the culture unless you are settling by a landmark.

What you're really going to be hurting for if you do wide-tall is happiness, so there will be many times where you're purposefully NOT growing certain cities (which is great, because then you work hammers). If you care about win turn times, Tradition will still get you to the finish line faster than liberty (even if you go 6 cities). In BNW, the Liberty's breakpoint where its bonuses value-wise out-weigh Tradition in 300 turns is somewhere around 8 cities for a normal start, 12 cities for a legendary-ish start, 6 cities for a bad start. On a normal start, you'd have to get an insane number of cities to finish sub-250 faster than Tradition. So, it's pretty much not going to actually beat out Tradition unless you war at some point (or you have an absolutely terrible capital).

Also in the tier description, you pointed that for that tier the Civ has guaranteed start( the other two things are present to the Rome's set of abilities). Imagine if you get a crappy capital with not enough hammers for the early-to-mid game and you can't snowball your hammers into being unstoppable production force. Game over.

The snowball is for your OTHER cities, so yes, if all of your early-wave cities are crappy, then there will be a problem (but there would have been a problem anyway, with any civ). The capital can be totally crappy for Rome and it's alright. You would just gold buy for one city (your capital), while it slowly chips away at the applicable national wonders. The crappier your capital for food, the more you want to spread early, you can't grow while hard building settlers anyway. The only start without hammers is a grassland start. And in that case you'll still be fine until mid-game, by that time you can start shipping back hammers if it's really a pure grass start.

These are the main things you look for in Rome. A coast (3 buildings), a river (3 buildings, although a lake would salvage 2 of the buildings), a mountain (1 building), ivory (1 building), sheep/cow (1 building), marble/stone (1 building), gold/silver (1 building). Also, make sure you don't build Rome on a hill! Windmills are pretty clutch for Rome.

The whole point of Rome is that you can more or less do anything you want and the bonus will be there to help you significantly. There are ways to min/max it, but you can really just go with the flow and the flow will be much smoother. There are only 3 maxims to playing Rome: 1) Try your best to avoid cash buying things Rome has built, 2) If you hit a key tech and want to build everywhere simultaneously, make sure you gold-buy it in Rome first, 3) Settle/conquer as many cities as you reasonably can without hitting happiness problems.
 
Good morning. Didn't go to university for this one. Rome is actually very very good at deity. I started a game with Rome (Pangea,Deity,Standart) just to try out stuff. Didn't really do any math there. Got nice plains start near some jungle. Got 5Luxes and 2 Cities with 2bananas in their 2 ring. Don't really want to post any images with my crappy laptop using Strategic View. Use the strategy you mentioned about landspacing and filling with cities ( I now like to call it Divide and Micromanage). Got liberty full - comerce - rationalism - order. Commerce + Big Ben is so overpowered for Romer... Got NC turn 77 with 3 cities then settled 4 (got of rivers). T260 may be 6-7 turns to finish a SV with 1700+bpt. Rush bought granary, all science building in capital still got enough money to buy a settler during my second wave (Double worker steal from Venice really helped, really like terrorizing Enrico).

Overall really nice civ. So fun to play. Sometimes I scratch my head during my games when my 3rd city needs an university and is build it in 17 turns.... no problem there.
I didn't fight anyone but I want to ask if the pillage/repari exploit is doable with Legions (Liberty + Pyramids). Also, i thought about Archipelago map and Rome. It is not that bad because you have food cargoe ships which can turn any start of your capital into nice one which means all your cities wil have nice production.

Thanks for the advices and nicely arguemented posts.
 
For me the best Civ for science on Deity has been maybe surprisingly The Inca. Their UI gives tons of food and you can place your cities next to mountains to get that extra +50% science.

In my last game (Pangaea + all normal except raging barbarians.) I went Tradition 4 cities. 3 of the 4 cities were besides a mountain. On turn 100 I was already leading in science. I went Full Tradition +Full Honor +Autocracy +Full Rationalism. I finished Tradition and Honor before I started Rationalism. I won science victory, but had lots of wars. Razed the conquered cities. Because of Honor finisher I made huge amounts of gold from wars.
 
EnterGodMode you didnt really go tradition at all then? What about religion?
Try to get the copper pantheon but Deity too OP for this :). Just builded faith from buildings/CSs (UA rulz :D), settled 1 prophet still got enough faith for 2 scientists and used the AIs religion for other faith purchases( i think i had 2pagodas and a mosque).

About the tradition - not really went 1 partonage, 1 commerce then rationalism, order. Didn't focus so much on culture. After order i was pciking random stuff.

About the inca - they were my first 3 or 4 victories on deity. Not very fast starts but the UI is so op u can have 4 cities grown to enourmous sizes still haveing 80 +hammers. Big fan of their style.
 
The DOF bonus is barely even an issue with Sweden, I sometimes forget it exists. GP gifting is where Sweden gets its kicks; with a phenomenal UU and a pretty good UU that you only need to build 1-2 of to get the full benefit of you really want to go domination. You're going to be ending up with a lot of excess Generals and captured Prophets that aren't doing you any good. Gift them to city-states and enjoy the benefits of practically automatic allies. If you dip into Honor for the faster General production then you can keep up with Greece in the battle for alliances.

They're still pretty neat on water maps too, you don't get the benefit of the UU's but the classic Frigate/Privateer combo is still so derply overpowered that it doesn't even matter and the amount of Admirals you don't need when you're playing that way is downright silly. Sweden is probably the most suited for Autocracy Diplo if you're into that sort of thing, I think.
Sweden is my favorite Civ I've probably put 1000 hours in on that civ alone. They are the only civ that I can successfully roll honor on deity. Your first GG goes to a culture CS your second to a maritime or faith CS. Once you hit t65-t70 you'll be making gold per kill. I could go more in depth with that but it's really beyond the scope of this thread. In addition you can get a faith pantheon reliably (the aurora one) and perhaps pair honor with holy warriors. Tundra starts give a lot of deer which are okay.
 
Sweden is my favorite Civ I've probably put 1000 hours in on that civ alone. They are the only civ that I can successfully roll honor on deity. Your first GG goes to a culture CS your second to a maritime or faith CS. Once you hit t65-t70 you'll be making gold per kill. I could go more in depth with that but it's really beyond the scope of this thread. In addition you can get a faith pantheon reliably (the aurora one) and perhaps pair honor with holy warriors. Tundra starts give a lot of deer which are okay.

There was some very weird strategy with Sweden in G&K but I can't recall exactly. It involved getting very nice faith generation adn gifting a lot of GPs to the city state while constantly having war. You get the reduced prophet costs and pilgramage. Burn your profphets 3 times to convert AIs' cities then with the last one you give it to the CS for a bunch of influence. Also training on a coastal CS gets you admirals to gift(presumably you didn't steal a worker). Something like that. It was well developed and all-around.

But nuff said this thread is more about discussing the tiers and the civs in them.
 
About Rome's UA, it's probably being underrated by some, but definitely overrated here.

The main problem with it are the conditions - 1) it's buildings only, and 2) it's only buildings already existing in the Capital.

On buildings only, think about the Hammer requirements that BNW added: Guilds, World's Fair (optional), Trade Units, Archaeologists. None of these are buildings. BNW actually cut down Ampi and Opera House requirements because they now sit and wait for Great Works. There's some indirect savings in that hammers saved mean more hammers later for other stuff, but the point is that you're only getting the bonus a fraction of the time. And you're getting it less often than in Vanilla. Because as far as buildings are concerned, I'm basically still only building Monument, Library, Granary, University, sometimes Shrine, Market, then Lighthouse/Stable/Stone Works depending whether the capital has that terrain. At least early.

For those late buildings, such as Public Schools, Research Labs, Hospitals, that's where the drawback of Capital-build buildings only come in. Your core 4-5 cities are mostly caught up on infrastructure by now and are waiting for techs to unlock these buidings. If you put all cities to produce it right when the tech is reached, then you get no bonus. So you have to buy the building in the Capital. Maybe you can do that, maybe you can't, but if you follow the supposed principle of Gold being worse than Hammers, you're being "inefficient" by buying in what's likely your most production heavy city.


Other than skipping over those two points, the comparison of Gold to Hammers on Tile Yield is pretty out of place. Tile yield is not the best place to get Gold, not even in the early game. Most all of your income will come from Trade Routes, which are giving 40-50 Gold before long. There is no real comparison to that in Hammers. Without even trying, your empire's Gold yield will generally double your Hammer yield, and with focus and Commerce discounts, you're tripling or quadrupling your Hammer yield and get a 40%-73% discount on expenditures. Big Ben has to be toned for BNW because of that. So all in all, Gold bonuses got better pound for pound, and Hammer bonuses worse.

Even if a civ were to be rated highly purely on Hammer bonuses, Germany should probably be ahead of Rome, Russia or any others. The free units from the UA often mean you don't need to build your own, and you build libraries instead of Archers. Then around Turn 120'ish the UB can be abused up to a 30-40% increase in Hammers, for Archaeologists or whatever you want to build, and at precisely the time where Rome's UA runs into the above problem.
 
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