Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Problem Statement

You have just arrived in a small country. Unfortunately a huge hurricane swept across the country a few days ago.

The country is made up of $n$ islands, numbered $1$ through $n$. Many bridges connected the islands, but all the bridges were washed away by a flood. People in the islands need new bridges to travel among the islands again.

The problem is cost. The country is not very wealthy. The government has to keep spending down. They asked you, a great programmer, to calculate the minimum cost to rebuild bridges. Write a program to calculate it!

Each bridge connects two islands bidirectionally. Each island $i$ has two parameters $d_i$ and $p_i$. An island $i$ can have at most $d_i$ bridges connected. The cost to build a bridge between an island $i$ and another island $j$ is calculated by $|p_i - p_j|$. Note that it may be impossible to rebuild new bridges within given limitations although people need to travel between any pair of islands over (a sequence of) bridges.

Input

The input is a sequence of datasets.
The number of datasets is less than or equal to $60$.
Each dataset is formatted as follows.

$n$
$p_1$ $d_1$
$p_2$ $d_2$
:
:
$p_n$ $d_n$

Everything in the input is an integer.
$n$ ($2 \leq n \leq 4{,}000$) on the first line indicates the number of islands.
Then $n$ lines follow, which contain the parameters of the islands.
$p_i$ ($1 \leq p_i \leq 10^9$) and $d_i$ ($1 \leq d_i \leq n$) denote the parameters of the island $i$.

The end of the input is indicated by a line with a single zero.

Output

For each dataset, output the minimum cost in a line if it is possible to rebuild bridges within given limitations in the dataset. Otherwise, output $-1$ in a line.

Sample Input

4
1 1
8 2
9 1
14 2
4
181 4
815 4
634 4
370 4
4
52 1
40 1
81 2
73 1
10
330 1
665 3
260 1
287 2
196 3
243 1
815 1
287 3
330 1
473 4
0

Output for the Sample Input

18
634
-1
916

Solution in Ruby (judge verdict: Runtime Error)

class Heap
	require 'forwardable'
	extend Forwardable

	def initialize
		@array = []
		@index = {}
	end

	def add(obj, key)
		@array << [obj, key]
		@index[obj] = @array.size - 1
		lift_up(@array.size - 1)
	end

	def swap(i, j)
		u = @array[i]
		v = @array[j]
		@index[u[0]], @index[v[0]] = j, i
		@array[i], @array[j] = v, u
	end

	def lift_up(i)
		return if i == 0
		j = (i - 1) / 2
		if (@array[i][1] <=> @array[j][1]) < 0
			swap(i, j)
			lift_up(j)
		end
	end

	def del_min
		raise "heap is empty!" if empty?
		min = @array[0]
		if size > 1
			swap(0, @array.size-1)
			@array.pop
			lift_down(0)
		else
			@array.pop
		end
		@index.delete(min[0])
		min
	end

	def inc_key(obj, diff)
		i = @index[obj]
		@array[i][1] += diff
		lift_down(i)
	end

	def dec_key(obj, diff)
		i = @index[obj]
		@array[i][1] -= diff
		lift_up(i)
	end

	def update_key(obj, new_key)
		i = @index[obj]
		return unless i
		return if (new_key <=> @array[i][1]) >= 0
		@array[i][1] = new_key
		lift_up(i)
	end

	def min_obj
		@array[0][0]
	end

	def min_key
		@array[0][1]
	end

	def lift_down(i)
		j = 2 * i + 1
		k = j + 1
		if k >= size
			return if j >= size
			if (@array[i][1] <=> @array[j][1]) > 0
				swap(i, j)
				lift_down(j)
			end
		else
			l = ((@array[j][1] <=> @array[k][1]) < 0 ? j : k)
			if (@array[i][1] <=> @array[l][1]) > 0
				swap(i, l)
				lift_down(l)
			end
		end
	end

	def_delegators :@array, :empty?, :size
end

module Graphical
	require 'set'

	def dijkstra(start)
		raise "start must be Enumerable" if !start.kind_of?(Enumerable)
		h = Heap.new
		reached = Set[*start.to_a]
		start.each{|s| h.add(s, 0)}

		dist = {}
		until h.empty?
			u, key = h.del_min
			#p [u, key]
			return key if block_given? && yield(u, key)
			dist[u] = key
			each_out_connection_of(u){|v, l|
				d = dist[u] + l
				if reached.include?(v)
					h.update_key(v, d)
				else
					h.add(v, d)
					reached << v
				end
			}
		end
		block_given? ? nil : dist
	end

	def bidir_dijkstra(s, t)
		f_dist = {}
		b_dist = {}

		f_heap = Heap.new
		b_heap = Heap.new

		f_heap.add(s, 0)
		b_heap.add(t, 0)

		f_reached = Set[s]
		b_reached = Set[t]

		f_current_dist = b_current_dist = 0
		best = Float::INFINITY

		loop {
			if !f_heap.empty?
				u, key = f_heap.del_min
				f_dist[u] = key
				f_current_dist = key
				each_out_connection_of(u){|v, l|
					d = f_dist[u] + l
					if b_dist[v]
						path_len = d + b_dist[v]
						best = path_len if path_len < best
					end
					if f_reached.include?(v)
						f_heap.update_key(v, d)
					else
						f_heap.add(v, d)
						f_reached << v
					end
				}
			end

			if !b_heap.empty?
				u, key = b_heap.del_min
				b_dist[u] = key
				b_current_dist = key
				each_in_connection_of(u){|v, l|
					d = b_dist[u] + l
					if f_dist[v]
						path_len = d + f_dist[v]
						best = path_len if path_len < best
					end
					if b_reached.include?(v)
						b_heap.update_key(v, d)
					else
						b_heap.add(v, d)
						b_reached << v
					end
				}
			end

			return best if f_current_dist + b_current_dist >= best
			return nil if f_heap.empty? && b_heap.empty?
		}
	end

end

loop {
	n = gets.to_i
	break if n == 0

	islands = (1..n).map{ gets.split.map &:to_i }.sort

	islands.extend Graphical

	def islands.each_out_connection_of(v)
		i, k, c = v
		return if i == self.size-1 || k == 0
		p1, d1 = self[i] 
		p2, d2 = self[i+1] 
		
		(0..[d2, k].min).each{|d_in|
			(0..d2-d_in).each{|d_out|
				next if d_in + d_out == 0
				new_k = k - d_in + d_out
				#next if (new_k == 0) ^ (i == self.size - 2)

				if d_out == 0
					next if i != self.size-2 && d_in > k - c
					yield([i+1, new_k, [c-(d_in-1), 1].max], k*(p2-p1))
				elsif d_in == 0
					yield([i+1, new_k, c+1], k*(p2-p1))
				else
					yield([i+1, new_k, [c-(d_in-1), 1].max], k*(p2-p1))
				end
			}
		}

	end

	p islands.dijkstra((1..islands[0][1]).map{|k| [0, k, 1]}){|v| v == [n-1, 0, 1]} || -1
}