How can I add Normal mapping to a Terrain custom shader?

I'm not a shader coder but I got a shader I liked here, the shader gets the object world position an sets a color gradient according to the vertical positions. I'm using it on a terrain and I can paint the textures as usual but I'd like to be able to use normal mapping too, so I tried to code it usisng the manual reference for surface shaders but didn't succeed on that part, also tried taking a look in the built-in shaders but as I'm not a shader coder, I couldn't figure out what I really had to do.

Here's the shader:

 Shader "Custom/HeightDependentTint" 
  {
    Properties 
    {
      _MainTex ("Base (RGB)", 2D) = "white" {}
      _Normal ("Normal (A)", 2D) = "bump" {}
      _HeightMin ("Height Min", Float) = -1
      _HeightMax ("Height Max", Float) = 1
      _ColorMin ("Tint Color At Min", Color) = (0,0,0,1)
      _ColorMax ("Tint Color At Max", Color) = (1,1,1,1)
    }
   
    SubShader
    {
      Tags { "RenderType"="Opaque" }
   
      CGPROGRAM
      #pragma surface surf Lambert
   
      sampler2D _MainTex;
      sampler2D _Normal;
      fixed4 _ColorMin;
      fixed4 _ColorMax;
      float _HeightMin;
      float _HeightMax;
   
      struct Input
      {
        float2 uv_MainTex;
        float2 uv_NormalMap;
        float3 worldPos;
      };
   
      void surf (Input IN, inout SurfaceOutput o) 
      {
        half4 c = tex2D (_MainTex, IN.uv_MainTex);
        float h = (_HeightMax-IN.worldPos.y) / (_HeightMax-_HeightMin);
        fixed4 tintColor = lerp(_ColorMax.rgba, _ColorMin.rgba, h);
        o.Albedo = c.rgb * tintColor.rgb;
        o.Alpha = c.a * tintColor.a;
        o.Normal = UnpackNormal (tex2D (_Normal, IN.uv_NormalMap));
      }
      ENDCG
    } 
    Fallback "Diffuse"
  }

Here's a picture of what I got: Here I have a nice brighter color on the top and gets darker in the bottom