```go
package main

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

// Global variables to store graph and state
var (
	adj        [][]Edge
	priorities []int
	ans        []int
	parent     []int
	counts     []int
	n          int
)

// Edge represents a connection to a child/parent with capacity
type Edge struct {
	to  int
	cap int
}

// Division represents a soldier division
type Division struct {
	id       int
	priority int
	time     int
}

// DSU find with path compression
// Finds the next available time slot
func find(i int) int {
	if parent[i] == i {
		return i
	}
	parent[i] = find(parent[i])
	return parent[i]
}

// DSU union
// Connects time i to j (usually i+1)
func union(i, j int) {
	rootI := find(i)
	rootJ := find(j)
	if rootI != rootJ {
		parent[rootI] = rootJ
	}
}

func main() {
	// Configure fast I/O
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)

	// Helper to read integers
	readInt := func() int {
		scanner.Scan()
		s := scanner.Bytes()
		x := 0
		for _, b := range s {
			x = x*10 + int(b-'0')
		}
		return x
	}

	if !scanner.Scan() {
		return
	}
	// Parse n
	s := scanner.Bytes()
	n = 0
	for _, b := range s {
		n = n*10 + int(b-'0')
	}

	priorities = make([]int, n+1)
	for i := 1; i <= n; i++ {
		priorities[i] = readInt()
	}

	adj = make([][]Edge, n+1)
	for i := 0; i < n-1; i++ {
		u := readInt()
		v := readInt()
		c := readInt()
		adj[u] = append(adj[u], Edge{to: v, cap: c})
		adj[v] = append(adj[v], Edge{to: u, cap: c})
	}

	ans = make([]int, n+1)

	// Pre-allocate DSU arrays
	// Size is sufficient for max possible time (approx N + N)
	// We use 2*N + 5000 to be safe.
	parent = make([]int, 2*n+5000)
	counts = make([]int, 2*n+5000)

	// Perform DFS from the capital (city 1)
	dfs(1, 0)

	// Print results
	out := bufio.NewWriter(os.Stdout)
	for i := 1; i <= n; i++ {
		if i > 1 {
			out.WriteByte(' ')
		}
		fmt.Fprint(out, ans[i])
	}
	out.WriteByte('\n')
	out.Flush()
}

// dfs processes the tree bottom-up.
// It returns a list of divisions currently at node u, sorted by priority.
// The 'time' field in the returned divisions represents the arrival time at u.
func dfs(u, p int) []Division {
	// Division starting at current city u arrives at time 0
	currentDiv := Division{id: u, priority: priorities[u], time: 0}
	merged := []Division{currentDiv}

	for _, e := range adj[u] {
		v := e.to
		if v == p {
			continue
		}

		// Get divisions from the subtree at v
		childList := dfs(v, u)
		
		// Process movement from v to u
		processedList := processEdge(childList, e.cap)
		
		// Merge the processed list into the current node's list
		merged = merge(merged, processedList)
	}

	// If we are at the capital, record the final arrival times
	if u == 1 {
		for _, d := range merged {
			ans[d.id] = d.time
		}
	}

	return merged
}

// processEdge computes the arrival times at the parent node given divisions at a child node.
// It simulates the capacity constraints of the edge.
func processEdge(divs []Division, capacity int) []Division {
	// Find the range of time slots we might touch
	maxT := 0
	for _, d := range divs {
		if d.time > maxT {
			maxT = d.time
		}
	}
	
	// Reset DSU and counts for the relevant range
	// The range is up to maxT + number of divisions waiting + buffer
	limit := maxT + len(divs) + 2
	if limit >= len(parent) {
		limit = len(parent) - 1
	}

	for i := 0; i <= limit; i++ {
		parent[i] = i
		counts[i] = 0
	}

	// Process divisions in priority order
	for i := range divs {
		// Find the earliest available departure time >= arrival time
		t := find(divs[i].time)
		
		// Division leaves at t, arrives at parent at t+1
		divs[i].time = t + 1
		
		// Update capacity usage for time t
		counts[t]++
		if counts[t] == capacity {
			// If capacity full, link t to t+1 so next find skips t
			union(t, t+1)
		}
	}
	return divs
}

// merge combines two sorted slices of Divisions into one sorted slice
func merge(a, b []Division) []Division {
	res := make([]Division, 0, len(a)+len(b))
	i, j := 0, 0
	for i < len(a) && j < len(b) {
		if a[i].priority < b[j].priority {
			res = append(res, a[i])
			i++
		} else {
			res = append(res, b[j])
			j++
		}
	}
	res = append(res, a[i:]...)
	res = append(res, b[j:]...)
	return res
}
```