Recently, I tried to solve a problem on Atcoder and came up with a solution. I got accepted but have no idea of its complexity. Does anyone know its complexity and when the worst case happens?

Problem:
Given an array with N integers A₁, A₂, ..., A_N and M intervals (L₁, R₁), ..., (L_M, R_M), you can perform the following operation arbitrary times:
Choose one of the M intervals (L_i, R_i) and add A_Li, A_Li + 1, ..., A_Ri by  + 1 or  - 1.
Is it possible to make all N integers zero?
N, M ≤ 10⁵

My solution:
First of all, if all L_i are different, we can uniquely determine how many times we should perform an operation on the interval (L_i, R_i) and whether we should choose  + 1 or  - 1.
Now, we try to avoid the same left bound. When we find two interval (L_i, R_i), (L_j, R_j) (R_i < R_j) with the same left bound, i.e. L_i = L_j, we change the second interval to (R_i + 1, R_j) (just imagine what happen if we add 1 to (L_j, R_j) and -1 to (L_i, R_i)). Because each interval never change its right bound and its left bound is increasing, so we won't do this infinitely.

Here's my implementation: First, we put all right bounds of intervals that have a left bound i into a vector bound[i]. Sort all bound[i]. Starting from bound[0] to bound[100000], we do something like
bound[bound[i][j]].push_back(bound[i][j+1]);
It's basically the operation shown in the following picture.
/predownloaded/ac/ca/acca90d2b71786f9164dd08325622b77d0d54eeb.png

At first, I thought it is a O(n²) but wasn't able to construct a O(n²) test case. After coding it, I got an AC and it only runs less than 100 ms. So what's the complexity?