Join N copies of a snippet to produce N^2 characters Challenge
Write the shortest snippet of code possible such that, when N copies of it are concatenated together, the number of characters output is N2. N will be a positive integer.
For example if the snippet was soln();, then running soln(); would print exactly 1 character, and running soln();soln(); would print exactly 4 characters, and running soln();soln();soln(); would print exactly 9 characters, etc.
Any characters may be in the output as long as the total number of characters is correct. To avoid cross-OS confusion, \r\n newlines are counted as one character.
Programs may not read their own source or read their file size or use other such loopholes. Treat this like a strict quine challenge.
The output may go to stdout or a file or a similar alternative. There is no input.
Comments in the code are fine, as is exiting mid-execution.
Any characters may be in the program. The shortest submission in bytes wins.
TECO, 4 bytes
V1\V

V prints the contents of the current line in the text buffer. 1\ inserts the string representation of the number 1 at the current position.
So on the Nth iteration of the program, the first V will output N - 1 copies of the character 1, then add another 1 to the text, then output N 1s.