You are given a series of trades. Each trade has a key, a value, a quantity, and a sequence number. For each trade, print the weighted moving average of all the trades for that particular key. Round your average to two decimal places. If the sequence number for any trade TT is less than the sequence number for any previous trade, throw out TT. Do not print anything for TT or factor it into your WMA.

M_{x+1} = {(M_x * Q_x)+(v_{x+1} * q_{x+1}) over Q_{x+1}}M x+1 = Q x+1 (M x *Q x )+(v x+1 *q x+1 )

Where M = weighted moving average, Q = total quantity, q = current quantity, and v = current value.

Input:

The input will be a semicolon-delimited string of trades, with each trade being comma-delimited. The parameters for each trade will be in order:

Key-Value Quantity Sequence number

Where key is a string, value is a rational floating-point number, quantity is a positive integer, and the sequence number is a positive integer.

Example:

1,2000,5,1;1,2050,5,2;2,3000,10,3

Output:

For each trade you do a calculation for, print on a new line {key}: {weighted moving average for key}

Example, from the example input above:

1: 2000 # key: CurrentAverage(1) = ((0*0)+(2000*5))/5 1: 2025 # key: CurrentAverage(1) = ((2000*5)+(2050*5))/10 2: 3000 # key: CurrentAverage(2) = ((0*0)+(3000*10))/10

Test 1

Test Input

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1,2000,5,1;1,2030,15,2;1,2000,10,1;2,2050,15,5;1,2067,8,6;2,2050,5,7

Expected Output

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1: 2000 1: 2022.5 2: 2050 1: 2035.21 2: 2050

Test 2

Test Input

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1,2000,5,3;2,2040,5,2

Expected Output

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1: 2000

Test 3

Test Input

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1,2000,5,2;1,2050,5,4

Expected Output

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1: 2000 1: 2025

Test 4

Test Input

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1,2000,5,1;2,2050,15,2

Expected Output

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1: 2000 2: 2050