Chesthetica

Chesthetica

Chesthetica

subscribers

A new if not unique KRBPPP vs kn five-move chess problem generated autonomously by Chesthetica using the computational creativity approach which doesn't use any kind of traditional AI or even deep learning. (Learn more about the DSNS here: https://arxiv.org/abs/1507.07058).

K7/8/2P5/5R2/kP5n/8/1BP5/8 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.14 5:48:35 PM
Solvability Estimate = Difficult

A seemingly earlier version of Chesthetica on a problem composed later (based on the date and time stamp) simply means that version may have been running on a different computer or operating system user account. White is over a rook's worth in material but the precise win in this position still needs to be found. Leave a comment below if you like. Over time, the tactics you see in these puzzles will help you improve your game.

Related Books: http://amazon.com/author/azlan_iqbal

What we have here is a 'KRBB vs kpp' #4 chess puzzle created by the prototype computer program, Chesthetica, using the computational creativity approach which doesn't use any kind of traditional AI or even deep learning. Chesthetica is able to generate mates in 3, mates in 4, mates in 5, study-like constructs and also compose problems using specific combinations of pieces fed into it. (Read more about it on ChessBase: https://en.chessbase.com/tagged?tag=Chesthetica).

3R1B2/8/8/8/5K2/p7/2p3B1/4k3 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.14 1:20:47 PM
Solvability Estimate = Moderate

Chesthetica composes only unique or new constructs (learn more here: https://en.chessbase.com/post/azlan-iqbal-introducing-chess-constructs). Try to solve this as quickly as you can. If you like it, please share with your friends. Take some time to study the analysis and you might appreciate the puzzle a little more.

Related Books: http://amazon.com/author/azlan_iqbal

A new if not unique KRBN vs kqnp mate in 5 chess problem generated autonomously by Chesthetica using the 'Digital Synaptic Neural Substrate' computational creativity approach which does not use any kind of deep learning. After years of development, Chesthetica is able to use the technology to express original creative thought in this domain. Note that it also never had millions of IBM or Google dollars behind it. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour. The position below contains 8 pieces which means it simply could not have been derived even from an existing endgame tablebase which is presently limited to 7 pieces.

8/8/3q4/1B6/4R3/2kn1N2/1p6/6K1 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.12 2:57:44 AM
Solvability Estimate = Easy

White actually has less material than Black yet still wins. The white army is down by about 2 (Shannon) pawn units in value. Do share and try out some of the others too. Feel free to copy the position into a chess engine and discover even more variations of the solution.

Related Books: http://amazon.com/author/azlan_iqbal

An original 'KRP vs kn' mate in 4 chess puzzle created by a computer program, Chesthetica, using the 'Digital Synaptic Neural Substrate' computational creativity method. It does not use endgame tablebases, artificial neural networks, machine learning or any kind of typical AI. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour.

8/KP6/7R/8/8/8/3n4/k7 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.11 9:52:31 PM
Solvability Estimate = Easy

White is significantly ahead in material. Try to solve this as quickly as you can. If you like it, please share with others. As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

A newly published and original KQB vs kn mate in 4 chess problem generated autonomously by Chesthetica using the DSNS computational creativity approach which doesn't use any kind of traditional AI. (Learn more about the DSNS here: https://arxiv.org/abs/1507.07058).

8/8/6K1/8/2Q5/8/2n2B2/k7 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.9 11:14:22 PM
Solvability Estimate = Difficult

Remarkably, Chesthetica never composes duplicate problems using its DSNS technology. Did you find this one interesting or have something else to say? Leave a comment below! Take some time to study the analysis and you might appreciate the puzzle a little more.

Related Books: http://amazon.com/author/azlan_iqbal

Published online for the first time, consider this KQRRB vs krbbp mate in 5the program, Chesthetica, using the approach known as the DSNS from the sub-field of AI, computational creativity. Any chess position over 7 pieces could not possibly have been derived from an endgame tablebase which today is limited to 7 pieces.

b3Q3/R7/4R3/8/3b4/3K2B1/r4p2/1k6 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.9 6:59:02 PM
Solvability Estimate = Easy

If you notice an earlier version of Chesthetica listed with a newer problem, that simply means an earlier version may have been running on a different computer or OS user account. Now, let's see what else there is to say. Give me a moment. Do share and try out some of the others too. Take some time to study the analysis and you might appreciate the puzzle a little more.

Related Books: http://amazon.com/author/azlan_iqbal

Here is a new 'KRRP vs kbnp' #4 chess puzzle created by Chesthetica using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, neural networks or any kind of machine learning found in traditional AI. Any chess position over 7 pieces could not possibly have been derived from an endgame tablebase which today is limited to 7 pieces.

7k/n7/3P4/1R6/6K1/6R1/6p1/7b w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.8 6:03:08 AM
Solvability Estimate = Moderate

White is significantly ahead in material. It looks like the solution might involve a pawn promotion. If this one is too easy or too difficult for you, try out some of the others. As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

An original 'KRBBBP vs kppppp' mate in 5 chess puzzle created by the prototype computer program, Chesthetica, using the approach known as the DSNS from the sub-field of AI, computational creativity. Chesthetica is able to generate mates in 3, mates in 4, mates in 5, study-like constructs and also compose problems using specific combinations of pieces fed into it. (Read more about it on ChessBase: https://en.chessbase.com/tagged?tag=Chesthetica).

1B6/8/3p3R/1BkpB3/4p3/1pP2p2/8/6K1 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.7 12:19:00 PM
Solvability Estimate = Easy

Chesthetica, especially if running on multiple computers or operating system user accounts, is capable of generating far too many compositions than can be published in a timely fashion here. The newer ones will therefore only be published some time later. This is why the composition date above does not match today's date. Chesthetica composes only unique or new constructs (learn more here: https://en.chessbase.com/post/azlan-iqbal-introducing-chess-constructs). Leave a comment below if you like. Solving chess puzzles like this is probably good for your health as it keeps your brain active. Nobody wants something like early-onset Alzheimer's.

Related Books: http://amazon.com/author/azlan_iqbal

Here is a new 'KRNNN vs kp' mate in 5 chess problem generated autonomously by the prototype computer program, Chesthetica, using the approach known as the DSNS from the sub-field of AI, computational creativity. There is no known limit to the quantity or type of compositions that can be generated.

8/2K5/4N1N1/1N1k4/8/5R2/5p2/8 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.7 3:33:18 AM
Solvability Estimate = Difficult

The chess problems are published chronologically based on the composition date and time. However, later compositions may have an earlier version of Chesthetica listed because more than one computer (not all running the same version of the program) is used. Chesthetica composes only unique or new constructs (learn more here: https://en.chessbase.com/post/azlan-iqbal-introducing-chess-constructs). Try to solve this puzzle. Do try some of the others in the series as well before you go. As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

Consider this 'KRBPP vs kpp' chess problem generated by a computer using the relatively new computational creativity approach called the 'DSNS'. Chesthetica is capable of composing positions that may otherwise take centuries or longer to arise in an actual game; so you can enjoy them right now instead. The largest (i.e. Lomonosov) tablebase today is for 7 pieces which contains over 500 trillion positions. With each additional piece, the number of possible positions increases exponentially. It is therefore impossible that this problem with 8 pieces could have been taken from such a database.

4R3/Pp6/7B/1k6/7p/5K2/P7/8 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.6 10:38:40 PM
Solvability Estimate = Difficult

Now, let's see what else there is to say. Give me a moment. Try to solve this puzzle. Do try some of the others in the series as well before you go. Over time, the tactics you see in these puzzles will help you improve your game.

Related Books: http://amazon.com/author/azlan_iqbal

A newly published and original KBBN vs kp five-move chess puzzle or problem (whichever you wish to call it) composed by a computer using the 'Digital Synaptic Neural Substrate' computational creativity method. It does not use endgame tablebases, artificial neural networks, machine learning or any kind of typical AI. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour.

4B3/8/k7/N3p3/2K5/8/7B/8 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.6 7:12:36 PM
Solvability Estimate = Easy

White is over a rook's worth in material but the precise win in this position still needs to be found. Try to solve this puzzle. Do try some of the others in the series as well before you go. Feel free to copy the position into a chess engine and discover even more variations of the solution.

Related Books: http://amazon.com/author/azlan_iqbal

Here is a new 'KRBNN vs krrp' chess problem generated autonomously by the program, Chesthetica, using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, deep learning or any kind of traditional AI. This position contains a total of 9 pieces. The largest endgame tablebase in existence today is for 7 pieces (containing over 500 trillion positions anyway) which means the problem could not have been taken from it regardless.

8/3N2rr/8/3Rpk2/6N1/5K2/8/5B2 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.6 5:28:49 PM
Solvability Estimate = Easy

Chesthetica, especially if running on multiple computers or operating system user accounts, is capable of generating far too many compositions than can be published in a timely fashion here. The newer ones will therefore only be published some time later. This is why the composition date above does not match today's date. White is significantly ahead in material. Try to solve this puzzle. Do try some of the others in the series as well before you go. Some of these problems may be trivial for you, especially if you're a club or master player but bear in mind that chess lovers can be found at all levels of play. So do check out some of the other problems. You can probably find something more to your taste.

Related Books: http://amazon.com/author/azlan_iqbal

This is an original 'KRBNPP vs krb' mate in 5 chess puzzle or problem (whichever you wish to call it) composed by Chesthetica using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, deep learning or any kind of traditional AI. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour. Noteworthy here is that a chess position with over 7 pieces could not have been derived or taken from an endgame tablebase because 7 pieces is the present limit.

kr6/5K2/N1P5/P7/6b1/7R/1B6/8 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.63 : Selangor, Malaysia
2018.3.6 3:33:32 PM
Solvability Estimate = Easy

The chess problems are published chronologically based on the composition date and time. However, later compositions may have an earlier version of Chesthetica listed because more than one computer (not all running the same version of the program) is used. Everything composed by Chesthetica is original. Try to solve this as quickly as you can. If you like it, please share with your friends. As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

A newly published and original KRBB vs krbn three-move chess puzzle or problem (whichever you wish to call it) composed by Chesthetica using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, deep learning or any kind of traditional AI. (Learn more about the DSNS here: https://arxiv.org/abs/1507.07058). Noteworthy here is that a chess position with over 7 pieces could not have been derived or taken from an endgame tablebase because 7 pieces is the present limit.

8/4B3/8/1r1B4/2RK4/1k6/n1b5/8 w - - 0 1
White to Play and Mate in 3
Chesthetica v10.63 : Selangor, Malaysia
2018.3.6 3:18:13 PM
Solvability Estimate = Easy

Material is even. Why not time yourself how long it took you to solve this? As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

Here is a new 'KQNPP vs kppppp' #4 chess problem generated autonomously by Chesthetica using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. The DSNS does not use endgame tablebases, neural networks or any kind of machine learning found in traditional artificial intelligence (AI). It also has nothing to do with deep learning. (Learn more about the DSNS here: https://arxiv.org/abs/1507.07058). Any chess position over 7 pieces could not possibly have been derived from an endgame tablebase which today is limited to 7 pieces.

8/8/1P4p1/3p4/6p1/2pp1k2/5P1Q/2N3K1 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.63 : Selangor, Malaysia
2018.3.5 8:09:31 AM
Solvability Estimate = Easy

White is over a rook's worth in material but the precise win in this position still needs to be found. Try to solve this as quickly as you can. If you like it, please share with your friends. Solving chess puzzles like this can also help improve your game.

Related Books: http://amazon.com/author/azlan_iqbal

A new if not unique KRR vs kr mate in 3 chess problem generated autonomously by Chesthetica using the approach known as the DSNS from the sub-field of AI, computational creativity. There is also no proven limit to the quantity or type of legal compositions that can be automatically generated.

K3k1r1/6R1/8/8/8/7R/8/8 w - - 0 1
White to Play and Mate in 3
Chesthetica v10.62 : Selangor, Malaysia
2018.3.5 7:15:08 AM
Solvability Estimate = Difficult

If you notice an earlier version of Chesthetica listed with a newer problem, that simply means an earlier version may have been running on a different computer or OS user account. Chesthetica composes only unique or new constructs (learn more here: https://en.chessbase.com/post/azlan-iqbal-introducing-chess-constructs). Why not time yourself how long it took you to solve this? Take some time to study the analysis and you might appreciate the puzzle a little more.

Related Books: http://amazon.com/author/azlan_iqbal

A new if not unique KRRB vs kp chess puzzle or problem (whichever you wish to call it) composed by a computer using the Digital Synaptic Neural Substrate AI computational creativity method. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour.

6R1/8/RK6/8/1k3B2/7p/8/8 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.62 : Selangor, Malaysia
2018.3.4 10:40:45 PM
Solvability Estimate = Easy

If you notice an earlier version of Chesthetica listed with a newer problem, that simply means an earlier version may have been running on a different computer or OS user account. Remarkably, Chesthetica never composes duplicate problems using its DSNS technology. Do you think you could have composed something better with these pieces? Share in the comments and let us know how long it took you. Note that not all the chess problems are like this. They cover quite the spectrum of solving ability and there are over a thousand published already.

Related Books: http://amazon.com/author/azlan_iqbal

Take a look at this 'KQBNP vs kbnn' mate in 5 chess puzzle created by the program, Chesthetica, using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. The DSNS does not use endgame tablebases, neural networks or any kind of machine learning found in traditional artificial intelligence (AI). It also has nothing to do with deep learning. Chesthetica is able to generate mates in 3, mates in 4, mates in 5, study-like constructs and also compose problems using specific combinations of pieces fed into it. (Read more about it on ChessBase: https://en.chessbase.com/tagged?tag=Chesthetica). Noteworthy here is that a chess position with over 7 pieces could not have been derived or taken from an endgame tablebase because 7 pieces is the present limit.

8/3nk3/2P5/QK6/5N2/4b3/1B6/2n5 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.62 : Selangor, Malaysia
2018.3.4 11:37:04 AM
Solvability Estimate = Difficult

If you notice an earlier version of Chesthetica listed with a newer problem, that simply means an earlier version may have been running on a different computer or OS user account. White is over a rook's worth in material but the precise win in this position still needs to be found. Try to solve this as quickly as you can. If you like it, please share with others. Note that not all the chess problems are like this. They cover quite the spectrum of solving ability and there are over a thousand published already.

Related Books: http://amazon.com/author/azlan_iqbal

A new if not unique KQBN vs kp four-move chess problem generated by a computer program, Chesthetica, using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, neural networks or any kind of machine learning found in traditional AI. (Learn more about the DSNS here: https://arxiv.org/abs/1507.07058).

3B4/k7/8/8/4Q3/8/4p3/K1N5 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.62 : Selangor, Malaysia
2018.3.3 5:15:47 AM
Solvability Estimate = Moderate

White has a decisive material advantage in this position but the winning sequence may not be immediately clear. Leave a comment below if you like. Some of these problems may be trivial for you, especially if you're a club or master player but bear in mind that chess lovers can be found at all levels of play. So do check out some of the other problems. You can probably find something more to your taste.

Related Books: http://amazon.com/author/azlan_iqbal

Consider this 'KQRNPPP vs krbpp' mate in 4 chess problem generated autonomously by the program, Chesthetica, using the Digital Synaptic Neural Substrate AI computational creativity method. Chesthetica is able to generate mates in 3, mates in 4, mates in 5, study-like constructs and also compose problems using specific combinations of pieces fed into it. (Read more about it on ChessBase: https://en.chessbase.com/tagged?tag=Chesthetica). The largest endgame tablebase in existence today is for 7 pieces (Lomonosov) which contains over 500 trillion positions, most of which have not been seen by human eyes. This problem with 12 pieces goes even beyond that and was therefore composed without any such help.

7R/1bP1kpPN/2P5/4r3/2Q5/8/3p4/3K4 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.62 : Selangor, Malaysia
2018.3.3 2:34:38 AM
Solvability Estimate = Difficult

Chesthetica, especially if running on multiple computers or operating system user accounts, is capable of generating far too many compositions than can be published in a timely fashion here. The newer ones will therefore only be published some time later. This is why the composition date above does not match today's date. Chesthetica composes only unique or new constructs (learn more here: https://en.chessbase.com/post/azlan-iqbal-introducing-chess-constructs). Try to solve this puzzle. Do try some of the others in the series as well before you go. As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

A newly published and original KNNPPP vs knp #4 chess puzzle or problem (whichever you wish to call it) composed by a computer using the 'Digital Synaptic Neural Substrate' computational creativity approach which does not use any kind of deep learning. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour. Noteworthy here is that a chess position with over 7 pieces could not have been derived or taken from an endgame tablebase because 7 pieces is the present limit.

1K6/6P1/1p2N3/8/P1k5/Pn6/4N3/8 w - - 0 1
White to Play and Mate in 4
Chesthetica v10.62 : Selangor, Malaysia
2018.3.2 2:27:21 PM
Solvability Estimate = Moderate

Remarkably, Chesthetica never composes duplicate problems using its DSNS technology. Try to solve this puzzle. Do try some of the others in the series as well before you go. Solving chess puzzles like this is probably good for your health as it keeps your brain active. Nobody wants something like early-onset Alzheimer's.

Related Books: http://amazon.com/author/azlan_iqbal

A newly published and original KRBN vs knp chess problem generated by the prototype computer program, Chesthetica, using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, neural networks or any kind of machine learning found in traditional AI.

8/5B1R/8/8/8/3N2K1/n1p5/3k4 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.62 : Selangor, Malaysia
2018.3.2 12:12:51 PM
Solvability Estimate = Moderate

White is over a rook's worth in material but the precise win in this position still needs to be found. Try to solve this puzzle. Do try some of the others in the series as well before you go. As a whole, these problems are intended to cater to players of all skill levels.

Related Books: http://amazon.com/author/azlan_iqbal

Here is a 'KRNP vs knp' chess problem generated autonomously by the prototype computer program, Chesthetica, using the DSNS computational creativity approach which doesn't use any kind of traditional AI. Chesthetica has the creative ability to compose positions that may otherwise take centuries to arise in an actual game, if ever. (Learn more about the DSNS here: https://arxiv.org/abs/1507.07058).

1K2k3/8/4p3/8/3PN3/8/8/3n1R2 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.62 : Selangor, Malaysia
2018.3.2 4:59:50 AM
Solvability Estimate = Moderate

White is significantly ahead in material. Did you find this one interesting or have something else to say? Leave a comment below! Solving chess puzzles like this is probably good for your health as it keeps your brain active. Nobody wants something like early-onset Alzheimer's.

Related Books: http://amazon.com/author/azlan_iqbal

An original 'KRRNN vs kqb' #5 chess puzzle created by Chesthetica using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. The DSNS does not use endgame tablebases, neural networks or any kind of machine learning found in traditional artificial intelligence (AI). It also has nothing to do with deep learning. Chesthetica is able to generate mates in 3, mates in 4, mates in 5, study-like constructs and also compose problems using specific combinations of pieces fed into it. (Read more about it on ChessBase: https://en.chessbase.com/tagged?tag=Chesthetica). Noteworthy here is that a chess position with over 7 pieces could not have been derived or taken from an endgame tablebase because 7 pieces is the present limit.

3qk3/4b3/6N1/8/8/1N6/5R2/4R1K1 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.62 : Selangor, Malaysia
2018.3.1 6:42:48 PM
Solvability Estimate = Easy

Chesthetica, especially if running on multiple computers or operating system user accounts, is capable of generating far too many compositions than can be published in a timely fashion here. The newer ones will therefore only be published some time later. This is why the composition date above does not match today's date. White is significantly ahead in material. If this one is too easy or too difficult for you, try out some of the others. Some of these problems may be trivial for you, especially if you're a club or master player but bear in mind that chess lovers can be found at all levels of play. So do check out some of the other problems. You can probably find something more to your taste.

Related Books: http://amazon.com/author/azlan_iqbal

Here is a new 'KQR vs kbbp' mate in 5 chess puzzle created by the program, Chesthetica, using the Digital Synaptic Neural Substrate (DSNS) computational creativity approach. It doesn't use endgame tablebases, deep learning or any kind of traditional AI. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour.

5b2/8/7R/8/3p1k2/7Q/1K6/5b2 w - - 0 1
White to Play and Mate in 5
Chesthetica v10.62 : Selangor, Malaysia
2018.3.1 4:37:25 PM
Solvability Estimate = Moderate

Okay, let me think for a minute if there's anything else to say here. Do share and try out some of the others too. Solving chess puzzles like this is probably good for your health as it keeps your brain active. Nobody wants something like early-onset Alzheimer's.

Related Books: http://amazon.com/author/azlan_iqbal

SHOW MORE

Created 1 year ago.

355 videos

CategoryGaming

The world's most advanced automatic chess problem composer.