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sql - Convert one row into multiple rows with fewer columns

I'd like to convert single rows into multiple rows in PostgreSQL, where some of the columns are removed. Here's an example of the current output:

name | st | ot | dt |
-----|----|----|----|
Fred | 8  | 2  | 3  |
Jane | 8  | 1  | 0  |
Samm | 8  | 0  | 6  |  
Alex | 8  | 0  | 0  |  

Using the following query:

SELECT
   name, st, ot, dt
FROM
   times;

And here's what I want:

name |  t | val |
-----|----|-----|
Fred | st |  8  |
Fred | ot |  2  |
Fred | dt |  3  |
Jane | st |  8  |
Jane | ot |  1  |
Samm | st |  8  |
Samm | dt |  6  |
Alex | st |  8  |

How can I modify the query to get the above desired output?

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SELECT
  times.name, x.t, x.val
FROM
  times cross join lateral (values('st',st),('ot',ot),('dt',dt)) as x(t,val)
WHERE
  x.val <> 0;

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