```go
package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {
	in := bufio.NewReader(os.Stdin)
	out := bufio.NewWriter(os.Stdout)
	defer out.Flush()

	var t int
	if _, err := fmt.Fscan(in, &t); err != nil {
		return
	}

	for i := 0; i < t; i++ {
		var n int
		fmt.Fscan(in, &n)

		// To minimize oneness |f(t) - g(t)|:
		// f(t) is number of subsequences with only '0's = 2^k - 1 (where k is count of '0's)
		// g(t) is number of subsequences with at least one '1' = (2^n - 1) - f(t)
		// We want f(t) approx g(t), so 2^k - 1 approx 2^{n-1}.
		// k = n-1 is optimal, giving oneness 1.
		// So we construct a string with n-1 '0's and 1 '1'.
		
		for j := 0; j < n-1; j++ {
			out.WriteByte('0')
		}
		out.WriteByte('1')
		out.WriteByte('\n')
	}
}
```