add new scripts

Scripts/analysis.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+"""
+
+@Author : Mohammad Imran SYED (mohammad-imran.syed@lip6.fr)
+
+This script also creates trace completeness plot for super-sniffers of size up to 10.
+
+It uses the num_packets.csv file created by the script initial_analysis.py. So you can run this script
+to modify or re-create figures instead of running initial_analysis.py again
+
+Run this script in the Analysis/ directory where num_packets.csv file is saved.
+
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+
+plt.rcParams['legend.title_fontsize'] = 'large'
+
+plt.rcParams['text.usetex'] = True
+plt.rcParams['font.family'] = 'DeJavu Serif'
+plt.rcParams['font.serif'] = ['Times New Roman']
+
+f = "num_packets.csv"
+df = pd.read_csv(f, delimiter='\t', squeeze=True)
+
+x=list()
+Y_MIN=list()
+Y_MAX=list()
+
+packets = df['Num_packets'].tolist()
+traces = df['Trace'].tolist()
+
+num_packets = [[] for _ in range(10)]
+
+num_packets[0] = packets[0:10]
+num_packets[1] = packets[10:55]
+num_packets[2] = packets[55:175]
+num_packets[3] = packets[175:385]
+num_packets[4] = packets[385:637]
+num_packets[5] = packets[637:847]
+num_packets[6] = packets[847:967]
+num_packets[7] = packets[967:1012]
+num_packets[8] = packets[1012:1022]
+num_packets[9] = packets[-1]
+
+for i in range(len(num_packets)-1):
+    j = num_packets[i]
+
+    min_packets = min(j)
+    max_packets = max(j)
+
+    x.append(i+1)
+    Y_MIN.append(min_packets)
+    Y_MAX.append(max_packets)
+
+x.append(i+2)
+Y_MIN.append(packets[-1])
+Y_MAX.append(packets[-1])
+
+y_min = [i / max(Y_MIN) for i in Y_MIN]
+y_max = [i / max(Y_MAX) for i in Y_MAX]
+
+NUM_1v1 = num_packets[0].sort()
+NUM_1v1 = num_packets[0][1:len(num_packets[0])-1]
+NUM_1v1 = [i / max(Y_MAX) for i in NUM_1v1]
+x1v1 = [x[0]] * len(NUM_1v1)
+
+NUM_2v2 = num_packets[1].sort()
+NUM_2v2 = num_packets[1][1:len(num_packets[1])-1]
+NUM_2v2 = [i / max(Y_MAX) for i in NUM_2v2]
+x2v2 = [x[1]] * len(NUM_2v2)
+
+NUM_3v3 = num_packets[2].sort()
+NUM_3v3 = num_packets[2][1:len(num_packets[2])-1]
+NUM_3v3 = [i / max(Y_MAX) for i in NUM_3v3]
+x3v3 = [x[2]] * len(NUM_3v3)
+
+NUM_4v4 = num_packets[3].sort()
+NUM_4v4 = num_packets[3][1:len(num_packets[3])-1]
+NUM_4v4 = [i / max(Y_MAX) for i in NUM_4v4]
+x4v4 = [x[3]] * len(NUM_4v4)
+
+NUM_5v5 = num_packets[4].sort()
+NUM_5v5 = num_packets[4][1:len(num_packets[4])-1]
+NUM_5v5 = [i / max(Y_MAX) for i in NUM_5v5]
+x5v5 = [x[4]] * len(NUM_5v5)
+
+NUM_6v6 = num_packets[5].sort()
+NUM_6v6 = num_packets[5][1:len(num_packets[5])-1]
+NUM_6v6 = [i / max(Y_MAX) for i in NUM_6v6]
+x6v6 = [x[5]] * len(NUM_6v6)
+
+NUM_7v7 = num_packets[6].sort()
+NUM_7v7 = num_packets[6][1:len(num_packets[6])-1]
+NUM_7v7 = [i / max(Y_MAX) for i in NUM_7v7]
+x7v7 = [x[6]] * len(NUM_7v7)
+
+NUM_8v8 = num_packets[7].sort()
+NUM_8v8 = num_packets[7][1:len(num_packets[7])-1]
+NUM_8v8 = [i / max(Y_MAX) for i in NUM_8v8]
+x8v8 = [x[7]] * len(NUM_8v8)
+
+NUM_9v9 = num_packets[8].sort()
+NUM_9v9 = num_packets[8][1:len(num_packets[8])-1]
+NUM_9v9 = [i / max(Y_MAX) for i in NUM_9v9]
+x9v9 = [x[8]] * len(NUM_9v9)
+
+fig=plt.figure()
+ax = fig.add_subplot(111)
+
+ax.plot(x, y_min, label=r'$\rm C_{\rm min}^{\rm m}$', marker='o', ms=4)
+ax.plot(x, y_max, label=r'$\rm C_{\rm max}^{\rm m}$', marker='x')
+
+ax.scatter(x1v1, NUM_1v1, marker='+', c='grey', s=15, label='Intermediate Completeness')
+ax.scatter(x2v2, NUM_2v2, marker='+', c='grey', s=15)
+ax.scatter(x3v3, NUM_3v3, marker='+', c='grey', s=15)
+ax.scatter(x4v4, NUM_4v4, marker='+', c='grey', s=15)
+ax.scatter(x5v5, NUM_5v5, marker='+', c='grey', s=15)
+ax.scatter(x6v6, NUM_6v6, marker='+', c='grey', s=15)
+ax.scatter(x7v7, NUM_7v7, marker='+', c='grey', s=15)
+ax.scatter(x8v8, NUM_8v8, marker='+', c='grey', s=15)
+ax.scatter(x9v9, NUM_9v9, marker='+', c='grey', s=15)
+
+
+ax.spines['right'].set_visible(False)
+ax.spines['top'].set_visible(False)
+ax.spines['left'].set_visible(False)
+ax.spines['bottom'].set_visible(False)
+ax.tick_params(axis='both', labelsize=20)
+
+plt.xticks(np.arange(0,11,1))
+plt.yticks(np.arange(0,1.1,0.1))
+
+plt.xlabel("Size of super-sniffer", fontsize=20)
+plt.ylabel("Completeness", fontsize=20)
+
+plt.legend(loc='best', frameon=False)
+plt.tight_layout()
+
+figure = "Completeness.pdf"
+plt.savefig(figure, format='pdf')
+
+
+num_packets[9] = [packets[-1]]
+comp = [[int(j/max(Y_MAX)*100) for j in i] for i in num_packets]
+comp = [item for sublist in comp for item in sublist]
+
+d = {'Trace':traces,'Completeness':comp}
+DF = pd.DataFrame(d)
+
+DF.to_csv('Completeness.csv', sep='\t', index=False, header=True)
+
+
+print("Figures created")
+print("ANALYSIS DONE")
+    

Scripts/analysis_gradient.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+"""
+
+@Author : Mohammad Imran SYED (mohammad-imran.syed@lip6.fr)
+
+This script also creates trace completeness plot  for super-sniffers of size up to 10,
+but it adds percentage of improvement brought by super-sniffer of each size to the plot.
+
+It uses the num_packets.csv file created by the script initial_analysis.py
+
+Run this script in the Analysis/ directory where num_packets.csv file is saved.
+
+"""
+
+import matplotlib.pyplot as plt
+import numpy as np
+import pandas as pd
+
+plt.rcParams['legend.title_fontsize'] = 'large'
+
+plt.rcParams['text.usetex'] = True
+plt.rcParams['font.family'] = 'DeJavu Serif'
+plt.rcParams['font.serif'] = ['Times New Roman']
+
+
+f = "num_packets.csv"
+df = pd.read_csv(f, delimiter='\t', squeeze=True)
+
+x=list()
+Y_MIN=list()
+Y_MAX=list()
+
+packets = df['Num_packets'].tolist()
+traces = df['Trace'].tolist()
+
+num_packets = [[] for _ in range(10)]
+
+num_packets[0] = packets[0:10]
+num_packets[1] = packets[10:55]
+num_packets[2] = packets[55:175]
+num_packets[3] = packets[175:385]
+num_packets[4] = packets[385:637]
+num_packets[5] = packets[637:847]
+num_packets[6] = packets[847:967]
+num_packets[7] = packets[967:1012]
+num_packets[8] = packets[1012:1022]
+num_packets[9] = packets[-1]
+
+for i in range(len(num_packets)-1):
+    j = num_packets[i]
+
+    min_packets = min(j)
+    max_packets = max(j)
+
+    x.append(i+1)
+    Y_MIN.append(min_packets)
+    Y_MAX.append(max_packets)
+
+x.append(i+2)
+Y_MIN.append(packets[-1])
+Y_MAX.append(packets[-1])
+
+y_min = [i / max(Y_MIN) for i in Y_MIN]
+y_max = [i / max(Y_MAX) for i in Y_MAX]
+
+delta = np.diff(y_max)
+delta = delta*100
+delta = np.round(delta,1)
+
+NUM_1v1 = num_packets[0].sort()
+NUM_1v1 = num_packets[0][1:len(num_packets[0])-1]
+NUM_1v1 = [i / max(Y_MAX) for i in NUM_1v1]
+x1v1 = [x[0]] * len(NUM_1v1)
+
+NUM_2v2 = num_packets[1].sort()
+NUM_2v2 = num_packets[1][1:len(num_packets[1])-1]
+NUM_2v2 = [i / max(Y_MAX) for i in NUM_2v2]
+x2v2 = [x[1]] * len(NUM_2v2)
+
+NUM_3v3 = num_packets[2].sort()
+NUM_3v3 = num_packets[2][1:len(num_packets[2])-1]
+NUM_3v3 = [i / max(Y_MAX) for i in NUM_3v3]
+x3v3 = [x[2]] * len(NUM_3v3)
+
+NUM_4v4 = num_packets[3].sort()
+NUM_4v4 = num_packets[3][1:len(num_packets[3])-1]
+NUM_4v4 = [i / max(Y_MAX) for i in NUM_4v4]
+x4v4 = [x[3]] * len(NUM_4v4)
+
+NUM_5v5 = num_packets[4].sort()
+NUM_5v5 = num_packets[4][1:len(num_packets[4])-1]
+NUM_5v5 = [i / max(Y_MAX) for i in NUM_5v5]
+x5v5 = [x[4]] * len(NUM_5v5)
+
+NUM_6v6 = num_packets[5].sort()
+NUM_6v6 = num_packets[5][1:len(num_packets[5])-1]
+NUM_6v6 = [i / max(Y_MAX) for i in NUM_6v6]
+x6v6 = [x[5]] * len(NUM_6v6)
+
+NUM_7v7 = num_packets[6].sort()
+NUM_7v7 = num_packets[6][1:len(num_packets[6])-1]
+NUM_7v7 = [i / max(Y_MAX) for i in NUM_7v7]
+x7v7 = [x[6]] * len(NUM_7v7)
+
+NUM_8v8 = num_packets[7].sort()
+NUM_8v8 = num_packets[7][1:len(num_packets[7])-1]
+NUM_8v8 = [i / max(Y_MAX) for i in NUM_8v8]
+x8v8 = [x[7]] * len(NUM_8v8)
+
+NUM_9v9 = num_packets[8].sort()
+NUM_9v9 = num_packets[8][1:len(num_packets[8])-1]
+NUM_9v9 = [i / max(Y_MAX) for i in NUM_9v9]
+x9v9 = [x[8]] * len(NUM_9v9)
+
+fig=plt.figure()
+ax = fig.add_subplot(111)
+ax.plot(x, y_max, label=r'$\rm C_{\rm max}^{\rm m}$', marker='x', ms=4, color='tab:orange')
+ax.plot(x, y_min, label=r'$\rm C_{\rm min}^{\rm m}$', marker='o', ms=4, color='tab:blue')
+
+ax.scatter(x1v1, NUM_1v1, marker='+', c='grey', s=14, label=r'$\rm C_{\rm .}^{\rm m}$')
+ax.scatter(x2v2, NUM_2v2, marker='+', c='grey', s=14)
+ax.scatter(x3v3, NUM_3v3, marker='+', c='grey', s=14)
+ax.scatter(x4v4, NUM_4v4, marker='+', c='grey', s=14)
+ax.scatter(x5v5, NUM_5v5, marker='+', c='grey', s=14)
+ax.scatter(x6v6, NUM_6v6, marker='+', c='grey', s=14)
+ax.scatter(x7v7, NUM_7v7, marker='+', c='grey', s=14)
+ax.scatter(x8v8, NUM_8v8, marker='+', c='grey', s=14)
+ax.scatter(x9v9, NUM_9v9, marker='+', c='grey', s=14)
+
+
+ax.spines['right'].set_visible(False)
+ax.spines['top'].set_visible(False)
+ax.spines['left'].set_visible(False)
+ax.spines['bottom'].set_visible(False)
+ax.tick_params(axis='both', labelsize=20)
+
+plt.xticks(np.arange(0,11,1))
+plt.yticks(np.arange(0,1.1,0.1))
+
+plt.xlabel("Size of super-sniffer", fontsize=20)
+plt.ylabel("Completeness", fontsize=20)
+
+plt.legend(loc='center', prop={'size': 14}, frameon=False)
+plt.tight_layout()
+
+for x,y in zip(x,delta):
+
+    label = "{:.1f}".format(y)
+    label = '+'+str(label)
+    plt.annotate(label, # this is the text
+                 (x+1,y_max[x]), # these are the coordinates to position the label
+                 textcoords="offset points", # how to position the text
+                 xytext=(-8,8), # distance from text to points (x,y)
+                 ha='center') # horizontal alignment can be left, right or center
+
+
+figure = "Completeness_gradient.pdf"
+plt.savefig(figure, format='pdf')
+
+print("Figures created")
+print("ANALYSIS DONE")
+    

Scripts/anonymize_csv.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+
+@Author : Mohammad Imran SYED (mohammad-imran.syed@lip6.fr)
+
+Script for extracting relevant information from .pcap files to save it in .txt files
+
+And also anonymize the traces (sender MAC addresses) and save them in AnonymizedTraces/ folder
+
+"""
+
+import time
+import hashlib
+import subprocess
+import os
+import pandas as pd
+import numpy as np
+import re
+
+class PCAP():
+    
+    def parsing(self, file):
+        
+        csvtraces = self.directory + 'CSVTraces/'
+        if not os.path.exists(csvtraces):
+            os.makedirs(csvtraces)
+        os.chmod(csvtraces, 0o777)
+        
+        tSharkOutputFile = csvtraces + file[0:len(file)-5] + '.txt'
+        tSharkOut = open(tSharkOutputFile, "wb")
+        tSharkInputFile = self.directory + file
+        tSharkCall = ['tshark', '-r', tSharkInputFile, '-Y', '!_ws.malformed and wlan_radio.channel==1', '-T', 'fields', '-E', 'header=y', '-E', 'separator=/t', '-e', 'frame.number', '-e', 'frame.time_epoch', '-e', 'frame.time_relative', '-e', 'wlan.fixed.timestamp', '-e', 'wlan_radio.signal_dbm', '-e', 'wlan_radio.channel', '-e', 'wlan.fc.type', '-e', 'wlan.fc.type_subtype', '-e', 'wlan.fc.retry', '-e', 'wlan.fcs', '-e', 'wlan.sa', '-e', 'wlan.seq', '-e', 'wlan.frag']
+        
+        tSharkProc = subprocess.Popen(tSharkCall, stdout=tSharkOut)
+        
+        tSharkProc.wait()
+        
+        tSharkOut.close()
+        
+        trace=pd.read_csv(tSharkOutputFile, delimiter='\t', squeeze=True)
+        
+        trace=trace.rename(columns={"frame.number":"Frame_number", "frame.time_epoch":"Frame_time_epoch", "frame.time_relative":"Frame_time_relative", "wlan.fixed.timestamp":"Fixed_timestamp", "wlan_radio.signal_dbm":"RSSI_dBm", "wlan_radio.channel":"Channel", "wlan.fc.type":"Frame_type", "wlan.fc.type_subtype":"Frame_subtype", "wlan.fc.retry":"Retransmission", "wlan.fcs":"Checksum", "wlan.sa":"Source_MAC_address", "wlan.seq":"Sequence_number", "wlan.frag":"Fragment_number"})
+
+        trace['Source_MAC_address'] = trace['Source_MAC_address'].fillna(0)
+        trace['Sequence_number'] = trace['Sequence_number'].fillna(0)
+
+        trace = trace.astype({"RSSI_dBm":int, "Channel":int, "Sequence_number":int})
+        trace.to_csv(tSharkOutputFile, index=False, header=True, sep='\t')    
+
+
+        anontraces = self.directory + 'AnonymizedTraces/'
+        if not os.path.exists(anontraces):
+            os.makedirs(anontraces)
+        os.chmod(anontraces, 0o777)
+        
+        c_size=1000
+        AnonymizedOutputFile = file[0:len(file)-5] + '.txt'
+        AnonymizedFilePath = anontraces + AnonymizedOutputFile
+        if os.path.exists(AnonymizedFilePath):
+            os.remove(AnonymizedFilePath)
+
+        for trace in pd.read_csv(tSharkOutputFile, delimiter='\t', chunksize=c_size):
+            #trace = pd.read_csv(tSharkOutputFile, delimiter='\t', squeeze=True)
+
+            all_src_mac = trace['Source_MAC_address'].tolist()
+            uniq_src_macs = np.unique(all_src_mac)         
+            
+            replacements_src = {}
+            
+            for mac in range(len(uniq_src_macs)):
+                replacements_src[uniq_src_macs[mac]]=str(uniq_src_macs[mac]).encode()
+                replacements_src[uniq_src_macs[mac]]=hashlib.sha512(replacements_src[uniq_src_macs[mac]]).hexdigest()
+                replacements_src[uniq_src_macs[mac]] = replacements_src[uniq_src_macs[mac]][:64]
+            
+            src_mac_anon=list()
+            
+            for i in range(len(all_src_mac)):
+                if all_src_mac[i] in replacements_src:
+                    all_src_mac[i] = replacements_src[all_src_mac[i]]
+                    src_mac_anon.append(all_src_mac[i])
+    
+            trace['Source_MAC_address'] = all_src_mac
+            if not os.path.exists(AnonymizedFilePath):
+                trace.to_csv(AnonymizedFilePath, index=False, header=True, sep='\t')
+            else:
+                trace.to_csv(AnonymizedFilePath, index=False, header=False, mode='a', sep='\t')
+    
+
+def main():
+
+    start = time.time()
+
+    anonymize_pcap = PCAP()
+    
+    anonymize_pcap.directory = 'Traces/' # the directory where you have saved the .pcap files
+
+    files = os.listdir(anonymize_pcap.directory)
+    files.sort()
+    files = files[2:len(files)-4]
+    files.sort(key=lambda f: int(re.sub('\D', '', f)))
+            
+    k=0
+    while k<len(files):
+        print("Anonymizing file : " + files[k])
+        anonymize_pcap.parsing(files[k])
+        k+=1
+        print("Anonymized")
+    
+    end = time.time()
+    
+    print("ALL FILES HAVE BEEN ANONYMIZED")
+    print("------------------------------------------------------------")
+    print("Time taken by the program in seconds: ", end-start)
+    print("------------------------------------------------------------")
+
+if __name__ == '__main__':
+    main()

Scripts/initial_analysis.py

+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+"""
+
+@Author : Mohammad Imran SYED (mohammad-imran.syed@lip6.fr)
+
+This script is used to create the trace completeness plot for super-sniffers of size up to 10.
+
+It creates all the necessary files for analysis those can be then used for
+creating plots, instead of doing all calculations of this in this script again and again.
+
+So you need to run this script first and then you analysis.py to modify plots
+according to your liking.
+
+Run this script in Analysis/ directory where you have the folders for all merged files
+
+"""
+
+import csv
+import os
+import matplotlib.pyplot as plt
+import numpy as np
+import re
+import time
+import pandas as pd
+
+plt.rcParams['legend.title_fontsize'] = 'large'
+#plt.rc('legend',fontsize=10) 
+
+plt.rcParams['text.usetex'] = True
+plt.rcParams['font.family'] = 'DeJavu Serif'
+plt.rcParams['font.serif'] = ['Times New Roman']
+
+start = time.time()
+
+f1 = "num_packets.csv"
+f1 = open(f1, "w+")
+
+x=list()
+Y_MIN=list()
+Y_MAX=list()
+num_packets = [[] for _ in range(10)]
+traces = [[] for _ in range(10)]
+
+packets = [[] for _ in range(10)] # lists of packets to find the maximum and minimum values for each combination
+
+folders = [f.path for f in os.scandir() if f.is_dir()]
+folders.sort(key=lambda f: int(re.sub('\D', '', f)))
+
+for k in range(len(folders)):
+    files = os.listdir(folders[k])
+    if files != []:
+        #files.sort()
+        folders.sort(key=lambda f: int(re.sub('\D', '', f)))
+        #print(files)
+
+    for l in range(len(files)):
+        if k==0:
+            file = open(folders[k]+"/"+files[l], "r+")
+            reader = csv.reader(file)
+            lines= len(list(reader)) - 1
+            file.close()                    
+            
+        else:
+            file = pd.read_csv(folders[k]+"/"+files[l], delimiter='\t', squeeze=True)
+            lines = file.values[0][1]
+        
+        if l==0:
+            packets[k].append(lines)
+        else:
+            packets[k][l] = packets[k][l] + lines
+ 
+ 
+        num_packets[k].append(lines)
+        traces[k].append(files[l][0:len(files[l])-4])
+
+
+for i in range(len(packets)):
+    min_packets = min(packets[i])
+    max_packets = max(packets[i])
+
+    x.append(i+1)
+    Y_MIN.append(min_packets)
+    Y_MAX.append(max_packets)
+
+
+f1.write("Trace\tNum_packets\n")
+for k in range(len(num_packets)):
+    for l in range(len(num_packets[k])):
+        f1.write(str(traces[k][l]) + "\t" + str(num_packets[k][l]) + "\n")
+f1.close()
+
+y_min = [i / max(Y_MIN) for i in Y_MIN]
+y_max = [i / max(Y_MAX) for i in Y_MAX]
+
+NUM_1v1 = num_packets[0].sort()
+NUM_1v1 = num_packets[0][1:len(num_packets[0])-1]
+NUM_1v1 = [i / max(Y_MAX) for i in NUM_1v1]
+x1v1 = [x[0]] * len(NUM_1v1)
+
+NUM_2v2 = num_packets[1].sort()
+NUM_2v2 = num_packets[1][1:len(num_packets[1])-1]
+NUM_2v2 = [i / max(Y_MAX) for i in NUM_2v2]
+x2v2 = [x[1]] * len(NUM_2v2)
+
+NUM_3v3 = num_packets[2].sort()
+NUM_3v3 = num_packets[2][1:len(num_packets[2])-1]
+NUM_3v3 = [i / max(Y_MAX) for i in NUM_3v3]
+x3v3 = [x[2]] * len(NUM_3v3)
+
+NUM_4v4 = num_packets[3].sort()
+NUM_4v4 = num_packets[3][1:len(num_packets[3])-1]
+NUM_4v4 = [i / max(Y_MAX) for i in NUM_4v4]
+x4v4 = [x[3]] * len(NUM_4v4)
+
+NUM_5v5 = num_packets[4].sort()
+NUM_5v5 = num_packets[4][1:len(num_packets[4])-1]
+NUM_5v5 = [i / max(Y_MAX) for i in NUM_5v5]
+x5v5 = [x[4]] * len(NUM_5v5)
+
+NUM_6v6 = num_packets[5].sort()
+NUM_6v6 = num_packets[5][1:len(num_packets[5])-1]
+NUM_6v6 = [i / max(Y_MAX) for i in NUM_6v6]
+x6v6 = [x[5]] * len(NUM_6v6)
+
+NUM_7v7 = num_packets[6].sort()
+NUM_7v7 = num_packets[6][1:len(num_packets[6])-1]
+NUM_7v7 = [i / max(Y_MAX) for i in NUM_7v7]
+x7v7 = [x[6]] * len(NUM_7v7)
+
+NUM_8v8 = num_packets[7].sort()
+NUM_8v8 = num_packets[7][1:len(num_packets[7])-1]
+NUM_8v8 = [i / max(Y_MAX) for i in NUM_8v8]
+x8v8 = [x[7]] * len(NUM_8v8)
+
+NUM_9v9 = num_packets[8].sort()
+NUM_9v9 = num_packets[8][1:len(num_packets[8])-1]
+NUM_9v9 = [i / max(Y_MAX) for i in NUM_9v9]
+x9v9 = [x[8]] * len(NUM_9v9)
+
+a=list()
+a.append(Y_MIN[-1]/max(Y_MIN))
+a.append(Y_MAX[-1]/max(Y_MAX))