Looking at this problem, I need to find for each prefix the minimum number of elements to change so that no subarray has GCD equal to its length.

Let me analyze: a subarray from l to r is "bad" if gcd(b_l,...,b_r) = r-l+1. The length of this subarray is r-l+1, so gcd = length.

Key insight: if gcd of a subarray equals its length, that means every element is divisible by (r-l+1). For a subarray of length 1, we need gcd(b_l) = 1, meaning b_l = 1. So any element equal to 1 must be changed.

For length 2: gcd(b_l, b_{l+1}) = 2, meaning both are even and their gcd is exactly 2.

This is a DP problem. Let me think about it as: process elements left to right, and use DP where f[i] = minimum changes for the first i elements.

For each position i, either we change a[i] (then f[i] = f[i-1] + 1, since we can change it to something that breaks all bad subarrays ending here), or we don't change a[i], and we need to ensure no bad subarray ends at i with all its elements unchanged.

If we don't change a[i], we need to check all possible subarray lengths L ending at i where a[i] is divisible by L, and ensure at least one element in positions [i-L+1, i] was changed.

Let me define dp[i] = min changes for prefix of length i. If we change position i: dp[i] = dp[i-1] + 1. If we don't change position i: dp[i] = dp[i-1] but we need to verify no bad subarray ending at i is fully unchanged. For each divisor L of a[i], if all elements in [i-L+1..i] are divisible by L and none were changed, that's bad.

This seems complex. Let me think with a different DP: dp[i] = minimum changes for first i elements. Track for each position i, the set of "dangerous" subarray lengths. We maintain GCD segments ending at position i.

For position i, the set of distinct GCDs of subarrays ending at i is O(log(a_i)). For each such GCD g with starting range [l..r], if g equals some length len = i-j+1 for j in [l..r], that's a constraint.

Let me implement a DP where dp[i] is the minimum number of changes for the first i elements such that no bad subarray exists entirely within unchanged elements. If we change element i, dp[i] = dp[i-1]+1. If we keep element i, dp[i] = dp[i-1] but we need that for every bad subarray ending at i (with all original elements), at least one position in it was changed. This means dp[i] = dp[i-1] only if for all bad subarrays [l..i], at least one element in [l..i-1] was changed OR equivalently dp[l-1] < dp[i-1] doesn't hold... Hmm, this is tricky.

Actually: if we keep position i, dp[i] must be ≥ dp[j-1]+0 but also we need that in [j..i], at least one is changed. The minimum changes in [j..i] is dp[i] - dp[j-1], and we need dp[i] - dp[j-1] ≥ 1 for each bad subarray [j..i].

So: dp[i] = min(dp[i-1]+1, max over all bad subarrays [j..i] of (dp[j-1]+1)).

Let me implement this with the standard GCD compression technique.

```go
package main

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

func gcd(a, b int) int {
	for b != 0 {
		a, b = b, a%b
	}
	return a
}

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

	var n int
	fmt.Fscan(reader, &n)
	a := make([]int, n)
	for i := range a {
		fmt.Fscan(reader, &a[i])
	}

	dp := make([]int, n+1) // dp[0]=0
	// gcd groups: list of (gcd_value, earliest_start_index)
	type pair struct{ g, start int }
	var groups []pair

	for i := 0; i < n; i++ {
		newGroups := []pair{}
		for _, p := range groups {
			g := gcd(p.g, a[i])
			if len(newGroups) > 0 && newGroups[len(newGroups)-1].g == g {
				continue
			}
			newGroups = append(newGroups, pair{g, p.start})
		}
		if len(newGroups) == 0 || newGroups[len(newGroups)-1].g != a[i] {
			newGroups = append(newGroups, pair{a[i], i})
		}
		groups = newGroups

		dp[i+1] = dp[i] + 1
		for _, p := range groups {
			length := i - p.start + 1
			if p.g%length == 0 {
				// bad subarray [p.start..i], need dp[p.start]+1
				if dp[p.start]+1 > dp[i+1] {
					dp[i+1] = dp[p.start] + 1
				}
			}
		}
		fmt.Fprintf(writer, "%d ", dp[i+1])
	}
}
```