diff --git a/README.md b/README.md
index fc7863a..b5a5ed7 100644
--- a/README.md
+++ b/README.md
@@ -17,3 +17,65 @@ Extra credit if you can find all FIVE bugs.
 - In the README, create a link to your shader toy solution with the bugs corrected
 - In the README, describe each bug you found and include a sentence about HOW you found it.
 - Make sure all three of your shadertoys are set to UNLISTED or PUBLIC (so we can see them!)
+
+
+# Final Result
+[Correct Shadertoy Link](https://www.shadertoy.com/view/lXfyD2)
+
+![image](https://github.com/user-attachments/assets/713999cf-661d-4e3d-88e9-ad71f65a406b)
+
+# Bugs
+## Bug1
+Typo of vec2 and uv.
+
+Found it thru shadertoy compiler error warning.
+
+## Bug2
+
+I fix Bug1 by changing 
+```
+vec uv2 = 2.0 * uv - vec2(1.0);
+```
+
+to
+
+```
+uv = 2.0 * uv - vec2(1.0);
+```
+
+So the Bug2 raycast(uv, dir, eye, ref); is resolved automatically.
+
+## Bug3 
+In function raycast, the H is computed like:
+```
+H *= len * iResolution.x / iResolution.x;
+```
+
+However, it should be computed as
+```
+H *= len * iResolution.x / iResolution.y;
+```
+
+How I found it:
+
+1. The shperes' shape is scaled in the horizontatl direction.
+2. The SDF of spheres is correct.
+3. So there is something wrong with ray's direction.
+4. Check the raycast function and each vector.
+5. iResolution.x / iResolution.x looks suspicious.
+
+
+## Bug4
+Compared to the correct scene, current scene has reflected color from other surfaces. So I guess there is something wrong with the reflected color.
+
+In line 75, the original shader get the dir to the reflect surface via ``` dir = reflect(eye, nor); ```
+
+It is wrong because the direction should be the next marching ray direction instead of eye direction. 
+
+```dir = reflect(dir, nor);```
+
+## Bug5
+The floor seems cut off in the scene compared to the correct one. It may because the rays stopped too early before reaching the floor.
+In the marching function, add more iterations for rays to expand farther.
+
+