For problem statement at 1000-1999/1600-1699/1680-1689/1689/problemE.txt this is a correct solution, but verifier at 1000-1999/1600-1699/1680-1689/1689/verifierE.go ends with test 12 failed
input:
1
2
17 4
expected: 1
17 5
got: 1
17 3

exit status 1 can you fix the verifier? ```go
package main

import (
	"bufio"
	"fmt"
	"math/bits"
	"os"
)

type dsu struct {
	p []int
	s []int
}

func newDsu(n int) *dsu {
	p := make([]int, n)
	s := make([]int, n)
	for i := 0; i < n; i++ {
		p[i] = i
		s[i] = 1
	}
	return &dsu{p: p, s: s}
}

func (d *dsu) find(x int) int {
	for x != d.p[x] {
		d.p[x] = d.p[d.p[x]]
		x = d.p[x]
	}
	return x
}

func (d *dsu) union(a, b int) {
	ra := d.find(a)
	rb := d.find(b)
	if ra == rb {
		return
	}
	if d.s[ra] < d.s[rb] {
		ra, rb = rb, ra
	}
	d.p[rb] = ra
	d.s[ra] += d.s[rb]
}

func connected(a []int) bool {
	n := len(a)
	start := -1
	for i := 0; i < n; i++ {
		if a[i] != 0 {
			start = i
			break
		}
	}
	if start == -1 {
		return false
	}
	d := newDsu(n)
	for b := 0; b < 30; b++ {
		prev := -1
		for i := 0; i < n; i++ {
			if ((a[i] >> b) & 1) != 0 {
				if prev == -1 {
					prev = i
				} else {
					d.union(prev, i)
				}
			}
		}
	}
	root := d.find(start)
	for i := 0; i < n; i++ {
		if a[i] != 0 && d.find(i) != root {
			return false
		}
		if a[i] == 0 {
			return false
		}
	}
	return true
}

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

	var t int
	fmt.Fscan(in, &t)
	for ; t > 0; t-- {
		var n int
		fmt.Fscan(in, &n)
		a := make([]int, n)
		for i := 0; i < n; i++ {
			fmt.Fscan(in, &a[i])
		}

		ops := 0
		for i := 0; i < n; i++ {
			if a[i] == 0 {
				a[i] = 1
				ops++
			}
		}

		if connected(a) {
			fmt.Fprintln(out, ops)
			for i := 0; i < n; i++ {
				if i > 0 {
					fmt.Fprint(out, " ")
				}
				fmt.Fprint(out, a[i])
			}
			fmt.Fprintln(out)
			continue
		}

		done := false
		for i := 0; i < n && !done; i++ {
			x := a[i]
			if x > 1 {
				a[i] = x - 1
				if connected(a) {
					fmt.Fprintln(out, ops+1)
					for j := 0; j < n; j++ {
						if j > 0 {
							fmt.Fprint(out, " ")
						}
						fmt.Fprint(out, a[j])
					}
					fmt.Fprintln(out)
					done = true
				}
				a[i] = x
				if done {
					break
				}
			}
			a[i] = x + 1
			if connected(a) {
				fmt.Fprintln(out, ops+1)
				for j := 0; j < n; j++ {
					if j > 0 {
						fmt.Fprint(out, " ")
					}
					fmt.Fprint(out, a[j])
				}
				fmt.Fprintln(out)
				done = true
			}
			a[i] = x
		}
		if done {
			continue
		}

		maxTZ := -1
		idxs := make([]int, 0)
		for i := 0; i < n; i++ {
			tz := bits.TrailingZeros(uint(a[i]))
			if tz > maxTZ {
				maxTZ = tz
				idxs = idxs[:0]
				idxs = append(idxs, i)
			} else if tz == maxTZ {
				idxs = append(idxs, i)
			}
		}
		i := idxs[0]
		j := idxs[1]
		a[i]--
		a[j]++
		fmt.Fprintln(out, ops+2)
		for k := 0; k < n; k++ {
			if k > 0 {
				fmt.Fprint(out, " ")
			}
			fmt.Fprint(out, a[k])
		}
		fmt.Fprintln(out)
	}
}
```