Spark SQL window function with complex condition
up vote
15
down vote
favorite
This is probably easiest to explain through example. Suppose I have a DataFrame of user logins to a website, for instance:
scala> df.show(5)
+----------------+----------+
| user_name|login_date|
+----------------+----------+
|SirChillingtonIV|2012-01-04|
|Booooooo99900098|2012-01-04|
|Booooooo99900098|2012-01-06|
| OprahWinfreyJr|2012-01-10|
|SirChillingtonIV|2012-01-11|
+----------------+----------+
only showing top 5 rows
I would like to add to this a column indicating when they became an active user on the site. But there is one caveat: there is a time period during which a user is considered active, and after this period, if they log in again, their became_active
date resets. Suppose this period is 5 days. Then the desired table derived from the above table would be something like this:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
|SirChillingtonIV|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-11| 2012-01-11|
+----------------+----------+-------------+
So, in particular, SirChillingtonIV's became_active
date was reset because their second login came after the active period expired, but Booooooo99900098's became_active
date was not reset the second time he/she logged in, because it fell within the active period.
My initial thought was to use window functions with lag
, and then using the lag
ged values to fill the became_active
column; for instance, something starting roughly like:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._
val window = Window.partitionBy("user_name").orderBy("login_date")
val df2 = df.withColumn("tmp", lag("login_date", 1).over(window))
Then, the rule to fill in the became_active
date would be, if tmp
is null
(i.e., if it's the first ever login) or if login_date - tmp >= 5
then became_active = login_date
; otherwise, go to the next most recent value in tmp
and apply the same rule. This suggests a recursive approach, which I'm having trouble imagining a way to implement.
My questions: Is this a viable approach, and if so, how can I "go back" and look at earlier values of tmp
until I find one where I stop? I can't, to my knowledge, iterate through values of a Spark SQL Column
. Is there another way to achieve this result?
sql apache-spark apache-spark-sql window-functions
add a comment |
up vote
15
down vote
favorite
This is probably easiest to explain through example. Suppose I have a DataFrame of user logins to a website, for instance:
scala> df.show(5)
+----------------+----------+
| user_name|login_date|
+----------------+----------+
|SirChillingtonIV|2012-01-04|
|Booooooo99900098|2012-01-04|
|Booooooo99900098|2012-01-06|
| OprahWinfreyJr|2012-01-10|
|SirChillingtonIV|2012-01-11|
+----------------+----------+
only showing top 5 rows
I would like to add to this a column indicating when they became an active user on the site. But there is one caveat: there is a time period during which a user is considered active, and after this period, if they log in again, their became_active
date resets. Suppose this period is 5 days. Then the desired table derived from the above table would be something like this:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
|SirChillingtonIV|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-11| 2012-01-11|
+----------------+----------+-------------+
So, in particular, SirChillingtonIV's became_active
date was reset because their second login came after the active period expired, but Booooooo99900098's became_active
date was not reset the second time he/she logged in, because it fell within the active period.
My initial thought was to use window functions with lag
, and then using the lag
ged values to fill the became_active
column; for instance, something starting roughly like:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._
val window = Window.partitionBy("user_name").orderBy("login_date")
val df2 = df.withColumn("tmp", lag("login_date", 1).over(window))
Then, the rule to fill in the became_active
date would be, if tmp
is null
(i.e., if it's the first ever login) or if login_date - tmp >= 5
then became_active = login_date
; otherwise, go to the next most recent value in tmp
and apply the same rule. This suggests a recursive approach, which I'm having trouble imagining a way to implement.
My questions: Is this a viable approach, and if so, how can I "go back" and look at earlier values of tmp
until I find one where I stop? I can't, to my knowledge, iterate through values of a Spark SQL Column
. Is there another way to achieve this result?
sql apache-spark apache-spark-sql window-functions
add a comment |
up vote
15
down vote
favorite
up vote
15
down vote
favorite
This is probably easiest to explain through example. Suppose I have a DataFrame of user logins to a website, for instance:
scala> df.show(5)
+----------------+----------+
| user_name|login_date|
+----------------+----------+
|SirChillingtonIV|2012-01-04|
|Booooooo99900098|2012-01-04|
|Booooooo99900098|2012-01-06|
| OprahWinfreyJr|2012-01-10|
|SirChillingtonIV|2012-01-11|
+----------------+----------+
only showing top 5 rows
I would like to add to this a column indicating when they became an active user on the site. But there is one caveat: there is a time period during which a user is considered active, and after this period, if they log in again, their became_active
date resets. Suppose this period is 5 days. Then the desired table derived from the above table would be something like this:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
|SirChillingtonIV|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-11| 2012-01-11|
+----------------+----------+-------------+
So, in particular, SirChillingtonIV's became_active
date was reset because their second login came after the active period expired, but Booooooo99900098's became_active
date was not reset the second time he/she logged in, because it fell within the active period.
My initial thought was to use window functions with lag
, and then using the lag
ged values to fill the became_active
column; for instance, something starting roughly like:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._
val window = Window.partitionBy("user_name").orderBy("login_date")
val df2 = df.withColumn("tmp", lag("login_date", 1).over(window))
Then, the rule to fill in the became_active
date would be, if tmp
is null
(i.e., if it's the first ever login) or if login_date - tmp >= 5
then became_active = login_date
; otherwise, go to the next most recent value in tmp
and apply the same rule. This suggests a recursive approach, which I'm having trouble imagining a way to implement.
My questions: Is this a viable approach, and if so, how can I "go back" and look at earlier values of tmp
until I find one where I stop? I can't, to my knowledge, iterate through values of a Spark SQL Column
. Is there another way to achieve this result?
sql apache-spark apache-spark-sql window-functions
This is probably easiest to explain through example. Suppose I have a DataFrame of user logins to a website, for instance:
scala> df.show(5)
+----------------+----------+
| user_name|login_date|
+----------------+----------+
|SirChillingtonIV|2012-01-04|
|Booooooo99900098|2012-01-04|
|Booooooo99900098|2012-01-06|
| OprahWinfreyJr|2012-01-10|
|SirChillingtonIV|2012-01-11|
+----------------+----------+
only showing top 5 rows
I would like to add to this a column indicating when they became an active user on the site. But there is one caveat: there is a time period during which a user is considered active, and after this period, if they log in again, their became_active
date resets. Suppose this period is 5 days. Then the desired table derived from the above table would be something like this:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
|SirChillingtonIV|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-11| 2012-01-11|
+----------------+----------+-------------+
So, in particular, SirChillingtonIV's became_active
date was reset because their second login came after the active period expired, but Booooooo99900098's became_active
date was not reset the second time he/she logged in, because it fell within the active period.
My initial thought was to use window functions with lag
, and then using the lag
ged values to fill the became_active
column; for instance, something starting roughly like:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._
val window = Window.partitionBy("user_name").orderBy("login_date")
val df2 = df.withColumn("tmp", lag("login_date", 1).over(window))
Then, the rule to fill in the became_active
date would be, if tmp
is null
(i.e., if it's the first ever login) or if login_date - tmp >= 5
then became_active = login_date
; otherwise, go to the next most recent value in tmp
and apply the same rule. This suggests a recursive approach, which I'm having trouble imagining a way to implement.
My questions: Is this a viable approach, and if so, how can I "go back" and look at earlier values of tmp
until I find one where I stop? I can't, to my knowledge, iterate through values of a Spark SQL Column
. Is there another way to achieve this result?
sql apache-spark apache-spark-sql window-functions
sql apache-spark apache-spark-sql window-functions
edited Sep 28 at 11:03
Community♦
11
11
asked Feb 24 '17 at 21:25
user4601931
2,00111323
2,00111323
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
25
down vote
accepted
Here is the trick. Import a bunch of functions:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions.{coalesce, datediff, lag, lit, min, sum}
Define windows:
val userWindow = Window.partitionBy("user_name").orderBy("login_date")
val userSessionWindow = Window.partitionBy("user_name", "session")
Find the points where new sessions starts:
val newSession = (coalesce(
datediff($"login_date", lag($"login_date", 1).over(userWindow)),
lit(0)
) > 5).cast("bigint")
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
Find the earliest date per session:
val result = sessionized
.withColumn("became_active", min($"login_date").over(userSessionWindow))
.drop("session")
With dataset defined as:
val df = Seq(
("SirChillingtonIV", "2012-01-04"), ("Booooooo99900098", "2012-01-04"),
("Booooooo99900098", "2012-01-06"), ("OprahWinfreyJr", "2012-01-10"),
("SirChillingtonIV", "2012-01-11"), ("SirChillingtonIV", "2012-01-14"),
("SirChillingtonIV", "2012-08-11")
).toDF("user_name", "login_date")
The result is:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-04| 2012-01-04| <- The first session for user
|SirChillingtonIV|2012-01-11| 2012-01-11| <- The second session for user
|SirChillingtonIV|2012-01-14| 2012-01-11|
|SirChillingtonIV|2012-08-11| 2012-08-11| <- The third session for user
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
+----------------+----------+-------------+
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
1
@SanchitGrover Ifdatediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates tonull
(first row in the frame) get 0.
– user6910411
Apr 15 at 10:19
Then how thisval sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?
– Sanchit Grover
Apr 15 at 12:02
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
25
down vote
accepted
Here is the trick. Import a bunch of functions:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions.{coalesce, datediff, lag, lit, min, sum}
Define windows:
val userWindow = Window.partitionBy("user_name").orderBy("login_date")
val userSessionWindow = Window.partitionBy("user_name", "session")
Find the points where new sessions starts:
val newSession = (coalesce(
datediff($"login_date", lag($"login_date", 1).over(userWindow)),
lit(0)
) > 5).cast("bigint")
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
Find the earliest date per session:
val result = sessionized
.withColumn("became_active", min($"login_date").over(userSessionWindow))
.drop("session")
With dataset defined as:
val df = Seq(
("SirChillingtonIV", "2012-01-04"), ("Booooooo99900098", "2012-01-04"),
("Booooooo99900098", "2012-01-06"), ("OprahWinfreyJr", "2012-01-10"),
("SirChillingtonIV", "2012-01-11"), ("SirChillingtonIV", "2012-01-14"),
("SirChillingtonIV", "2012-08-11")
).toDF("user_name", "login_date")
The result is:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-04| 2012-01-04| <- The first session for user
|SirChillingtonIV|2012-01-11| 2012-01-11| <- The second session for user
|SirChillingtonIV|2012-01-14| 2012-01-11|
|SirChillingtonIV|2012-08-11| 2012-08-11| <- The third session for user
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
+----------------+----------+-------------+
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
1
@SanchitGrover Ifdatediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates tonull
(first row in the frame) get 0.
– user6910411
Apr 15 at 10:19
Then how thisval sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?
– Sanchit Grover
Apr 15 at 12:02
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
add a comment |
up vote
25
down vote
accepted
Here is the trick. Import a bunch of functions:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions.{coalesce, datediff, lag, lit, min, sum}
Define windows:
val userWindow = Window.partitionBy("user_name").orderBy("login_date")
val userSessionWindow = Window.partitionBy("user_name", "session")
Find the points where new sessions starts:
val newSession = (coalesce(
datediff($"login_date", lag($"login_date", 1).over(userWindow)),
lit(0)
) > 5).cast("bigint")
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
Find the earliest date per session:
val result = sessionized
.withColumn("became_active", min($"login_date").over(userSessionWindow))
.drop("session")
With dataset defined as:
val df = Seq(
("SirChillingtonIV", "2012-01-04"), ("Booooooo99900098", "2012-01-04"),
("Booooooo99900098", "2012-01-06"), ("OprahWinfreyJr", "2012-01-10"),
("SirChillingtonIV", "2012-01-11"), ("SirChillingtonIV", "2012-01-14"),
("SirChillingtonIV", "2012-08-11")
).toDF("user_name", "login_date")
The result is:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-04| 2012-01-04| <- The first session for user
|SirChillingtonIV|2012-01-11| 2012-01-11| <- The second session for user
|SirChillingtonIV|2012-01-14| 2012-01-11|
|SirChillingtonIV|2012-08-11| 2012-08-11| <- The third session for user
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
+----------------+----------+-------------+
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
1
@SanchitGrover Ifdatediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates tonull
(first row in the frame) get 0.
– user6910411
Apr 15 at 10:19
Then how thisval sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?
– Sanchit Grover
Apr 15 at 12:02
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
add a comment |
up vote
25
down vote
accepted
up vote
25
down vote
accepted
Here is the trick. Import a bunch of functions:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions.{coalesce, datediff, lag, lit, min, sum}
Define windows:
val userWindow = Window.partitionBy("user_name").orderBy("login_date")
val userSessionWindow = Window.partitionBy("user_name", "session")
Find the points where new sessions starts:
val newSession = (coalesce(
datediff($"login_date", lag($"login_date", 1).over(userWindow)),
lit(0)
) > 5).cast("bigint")
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
Find the earliest date per session:
val result = sessionized
.withColumn("became_active", min($"login_date").over(userSessionWindow))
.drop("session")
With dataset defined as:
val df = Seq(
("SirChillingtonIV", "2012-01-04"), ("Booooooo99900098", "2012-01-04"),
("Booooooo99900098", "2012-01-06"), ("OprahWinfreyJr", "2012-01-10"),
("SirChillingtonIV", "2012-01-11"), ("SirChillingtonIV", "2012-01-14"),
("SirChillingtonIV", "2012-08-11")
).toDF("user_name", "login_date")
The result is:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-04| 2012-01-04| <- The first session for user
|SirChillingtonIV|2012-01-11| 2012-01-11| <- The second session for user
|SirChillingtonIV|2012-01-14| 2012-01-11|
|SirChillingtonIV|2012-08-11| 2012-08-11| <- The third session for user
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
+----------------+----------+-------------+
Here is the trick. Import a bunch of functions:
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions.{coalesce, datediff, lag, lit, min, sum}
Define windows:
val userWindow = Window.partitionBy("user_name").orderBy("login_date")
val userSessionWindow = Window.partitionBy("user_name", "session")
Find the points where new sessions starts:
val newSession = (coalesce(
datediff($"login_date", lag($"login_date", 1).over(userWindow)),
lit(0)
) > 5).cast("bigint")
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
Find the earliest date per session:
val result = sessionized
.withColumn("became_active", min($"login_date").over(userSessionWindow))
.drop("session")
With dataset defined as:
val df = Seq(
("SirChillingtonIV", "2012-01-04"), ("Booooooo99900098", "2012-01-04"),
("Booooooo99900098", "2012-01-06"), ("OprahWinfreyJr", "2012-01-10"),
("SirChillingtonIV", "2012-01-11"), ("SirChillingtonIV", "2012-01-14"),
("SirChillingtonIV", "2012-08-11")
).toDF("user_name", "login_date")
The result is:
+----------------+----------+-------------+
| user_name|login_date|became_active|
+----------------+----------+-------------+
| OprahWinfreyJr|2012-01-10| 2012-01-10|
|SirChillingtonIV|2012-01-04| 2012-01-04| <- The first session for user
|SirChillingtonIV|2012-01-11| 2012-01-11| <- The second session for user
|SirChillingtonIV|2012-01-14| 2012-01-11|
|SirChillingtonIV|2012-08-11| 2012-08-11| <- The third session for user
|Booooooo99900098|2012-01-04| 2012-01-04|
|Booooooo99900098|2012-01-06| 2012-01-04|
+----------------+----------+-------------+
answered Feb 24 '17 at 22:51
user6910411
32.1k86692
32.1k86692
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
1
@SanchitGrover Ifdatediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates tonull
(first row in the frame) get 0.
– user6910411
Apr 15 at 10:19
Then how thisval sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?
– Sanchit Grover
Apr 15 at 12:02
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
add a comment |
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
1
@SanchitGrover Ifdatediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates tonull
(first row in the frame) get 0.
– user6910411
Apr 15 at 10:19
Then how thisval sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?
– Sanchit Grover
Apr 15 at 12:02
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
I know it has been a long time, but can you help me understand the coalesce part of the solution??
– Sanchit Grover
Apr 15 at 8:33
1
1
@SanchitGrover If
datediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates to null
(first row in the frame) get 0.– user6910411
Apr 15 at 10:19
@SanchitGrover If
datediff($"login_date", lag($"login_date", 1).over(userWindow))
evaluates to null
(first row in the frame) get 0.– user6910411
Apr 15 at 10:19
Then how this
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?– Sanchit Grover
Apr 15 at 12:02
Then how this
val sessionized = df.withColumn("session", sum(newSession).over(userWindow))
is increasing the count?– Sanchit Grover
Apr 15 at 12:02
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
It is a cumulative sum of values in set {0, 1}.
– user6910411
Apr 15 at 12:04
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
I would double vote this answer if I could, thx!
– Madhava Carrillo
Nov 22 at 10:25
add a comment |
Thanks for contributing an answer to Stack Overflow!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstackoverflow.com%2fquestions%2f42448564%2fspark-sql-window-function-with-complex-condition%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown