You are given a task to integrate an existing React component in the codebase

The codebase should support:
- shadcn project structure  
- Tailwind CSS
- Typescript

If it doesn't, provide instructions on how to setup project via shadcn CLI, install Tailwind or Typescript.

Determine the default path for components and styles. 
If default path for components is not /components/ui, provide instructions on why it's important to create this folder
Copy-paste this component to /components/ui folder:
```tsx
modern-stunning-sign-in.tsx
"use client";

import * as React from "react";
import { useState } from "react";

const SignIn1 = () => {
  const [email, setEmail] = React.useState("");
  const [password, setPassword] = React.useState("");
  const [error, setError] = React.useState("");

  const validateEmail = (email: string) => {
    return /^[^\s@]+@[^\s@]+\.[^\s@]+$/.test(email);
  };

  const handleSignIn = () => {
    if (!email || !password) {
      setError("Please enter both email and password.");
      return;
    }
    if (!validateEmail(email)) {
      setError("Please enter a valid email address.");
      return;
    }
    setError("");
    alert("Sign in successful! (Demo)");
  };

  return (
    <div className="min-h-screen flex flex-col items-center justify-center bg-[#121212] relative overflow-hidden w-full rounded-xl">
      {/* Centered glass card */}
      <div className="relative z-10 w-full max-w-sm rounded-3xl bg-gradient-to-r from-[#ffffff10] to-[#121212] backdrop-blur-sm  shadow-2xl p-8 flex flex-col items-center">
        {/* Logo */}
        <div className="flex items-center justify-center w-12 h-12 rounded-full bg-white/20 mb-6 shadow-lg">
          <img src="https://cdn.21st.dev/assets/localized/92db5b0ae3b97eefb3308b3ad28645caaaf0a5125369b81c7cb8a8df1a610043.svg" />
        </div>
        {/* Title */}
        <h2 className="text-2xl font-semibold text-white mb-6 text-center">
          HextaUI
        </h2>
        {/* Form */}
        <div className="flex flex-col w-full gap-4">
          <div className="w-full flex flex-col gap-3">
            <input
              placeholder="Email"
              type="email"
              value={email}
              className="w-full px-5 py-3 rounded-xl  bg-white/10 text-white placeholder-gray-300 text-sm focus:outline-none focus:ring-2 focus:ring-gray-400"
              onChange={(e) => setEmail(e.target.value)}
            />
            <input
              placeholder="Password"
              type="password"
              value={password}
              className="w-full px-5 py-3 rounded-xl  bg-white/10 text-white placeholder-gray-300 text-sm focus:outline-none focus:ring-2 focus:ring-gray-400"
              onChange={(e) => setPassword(e.target.value)}
            />
            {error && (
              <div className="text-sm text-red-400 text-left">{error}</div>
            )}
          </div>
          <hr className="opacity-10" />
          <div>
            <button
              onClick={handleSignIn}
              className="w-full bg-white/10 text-white font-medium px-5 py-3 rounded-full shadow hover:bg-white/20 transition mb-3  text-sm"
            >
              Sign in
            </button>
            {/* Google Sign In */}
            <button className="w-full flex items-center justify-center gap-2 bg-gradient-to-b from-[#232526] to-[#2d2e30] rounded-full px-5 py-3 font-medium text-white shadow hover:brightness-110 transition mb-2 text-sm">
              <img
                src="https://cdn.21st.dev/assets/mirror/38/38146bfd9eff6dbf0d74771f2e625c70d87d3770e0d080dbb6e50db1d5403f46.svg"
                alt="Google"
                className="w-5 h-5"
              />
              Continue with Google
            </button>
            <div className="w-full text-center mt-2">
              <span className="text-xs text-gray-400">
                Don&apos;t have an account?{" "}
                <a
                  href="#"
                  className="underline text-white/80 hover:text-white"
                >
                  Sign up, it&apos;s free!
                </a>
              </span>
            </div>
          </div>
        </div>
      </div>
      {/* User count and avatars */}
      <div className="relative z-10 mt-12 flex flex-col items-center text-center">
        <p className="text-gray-400 text-sm mb-2">
          Join <span className="font-medium text-white">thousands</span> of
          developers who are already using HextaUI.
        </p>
        <div className="flex">
          <img
            src="https://cdn.21st.dev/assets/mirror/a6/a634d4f02fe5b77804943c1d74b8d70e35ffe26454e0e9af9717432a2c72bfde.jpg"
            alt="user"
            className="w-8 h-8 rounded-full border-2 border-[#181824] object-cover"
          />
          <img
            src="https://cdn.21st.dev/assets/mirror/d8/d8dab29a5736d5c2b0084d720d3db02c785560071609be501541922928fdf831.jpg"
            alt="user"
            className="w-8 h-8 rounded-full border-2 border-[#181824] object-cover"
          />
          <img
            src="https://cdn.21st.dev/assets/mirror/d1/d1a3e08d4e37d6ee2b7de1db8df87c1dc7acd8ffb004caaf980917de518a60c9.jpg"
            alt="user"
            className="w-8 h-8 rounded-full border-2 border-[#181824] object-cover"
          />
          <img
            src="https://cdn.21st.dev/assets/mirror/f0/f07b84f12ef125cbb837a7bd64da401992f5f62bd55fee10d01cd3dcc8abae80.jpg"
            alt="user"
            className="w-8 h-8 rounded-full border-2 border-[#181824] object-cover"
          />
        </div>
      </div>
    </div>
  );
};

export { SignIn1 };

export default SignIn1;


demo.tsx
import { SignIn1 } from "@/components/ui/modern-stunning-sign-in";

function Demo() {
  return <SignIn1 />;
}

export { Demo };

export default Demo;

```

Implementation Guidelines
 1. Analyze the component structure and identify all required dependencies
 2. Review the component's argumens and state
 3. Identify any required context providers or hooks and install them
 4. Questions to Ask
 - What data/props will be passed to this component?
 - Are there any specific state management requirements?
 - Are there any required assets (images, icons, etc.)?
 - What is the expected responsive behavior?
 - What is the best place to use this component in the app?

Steps to integrate
 0. Copy paste all the code above in the correct directories
 1. Install external dependencies
 2. Fill image assets with Unsplash stock images you know exist
 3. Use lucide-react icons for svgs or logos if component requires them