PROC.OF THE IEEE,NOVEMBER 1998 was collected among Census Bureau employees,while SD-1 was collected among high-school students.Drawing sensi- > 68/79b641 ble conclusions from learning experiments requires that the b 757863485 result be independent of the choice of training set and test among the complete set of samples.Therefore it was nec- 2【79 7 a 86 essary to build a new database by mixing NISTss datasets. SD-1 contains 5s,517 digit images written by 5yy dif- 4819018894 ferent writers.In contrast to SD-3,where blocks of data 子61&6 4/5b0 from each writer appeared in sequence,the data in SD-1 is scrambled.N riter identities for SD-1 are available and we 7592658197 used this information to unscramble the writers.N e then split sD-1 in twoe characters written by the first 5y writers 2久22234480 went into our new training set.The remaining 5y writers 038073857 were placed in our test set.Thus we had two sets with nearly 3y,yyy examples each.The new training set was 01446024a completed with enough examples from SD-3,starting at pattern c y,to make a full set of Py,yyy training patterns. 7/281o98b Similarly,the new test set was completed with SD-3 exam- ples starting at pattern c 35,yyy to make a full set with Aig..Size-normalized examples from the MNIST database. Py,yyy test patterns.In the experiments described here,we only used a subset of 1y,yyy test images(5,yyy from SD-1 and 5,yyy from SD-3),but we used the full Py,yyy training three,y.yyyl for the next three,y.yyyy5 for the next 4, samples.The resulting database was called the Modified and y.yyyyl thereafter.Before each iteration,the diagonal NIST,or MNIST,dataset. Hessian approximation was reevaluated on 5yy samples,as The original black and white (bilevel)images were size described in Appendix C and kept fixed during the entire normalized to fit in a I yxy pixel box while preserving iteration.The parameter l was set to y.y.The resulting their aspect ratio.The resulting images contain grey lev- effective learning rates during the first pass varied between els as result of the anti-aliasing (image interpolation)tech- approximately 7 x 1y-2 and y.ylP over the set of parame- nique used by the normalization algorithm.Three ver- ters.The test error rate stabilizes after around ly passes sions of the database were used.In the first version, through the training set at y.95%.The error rate on the the images were centered in a IsxIs image by comput- training set reaches y.35%after 19 passes.Many authors ing the center of mass of the pixels,and translating the have reported observing the common phenomenon of over- image so as to position this point at the center of the training when training neural networks or other adaptive IsxIs field.In some instances,this IsxIs field was ex- algorithms on various tasks.N hen over-training occurs, tended to 31 x3 with background pixels.This version of the training error keeps decreasing over time,but the test the database will be referred to as the regular database. error goes through a minimum and starts increasing after In the second version of the database,the character im- a certain number of iterations.N hile this phenomenon is ages were deslanted and cropped down to yxy pixels im- very common,it was not observed in our case as the learn- ages.The deslanting computes the second moments of in- ing curves in figure 5 show.A possible reason is that the ertia of the pixels(counting a foreground pixel as 1 and a learning rate was kept relatively large.The effect of this is background pixel as y),and shears the image by horizon- that the weights never settle down in the local minimum tally shifting the lines so that the principal axis is verti- but keep oscillating randomly.Because of those fluctua- cal.This version of the database will be referred to as the tions,the average cost will be lower in a broader minimum. deslanted database.In the third version of the database Therefore,stochastic gradient will have a similar effect as used in some early experiments,the images were reduced a regularization term that favors broader minima.Broader to 1Px1P pixels.The regular database (Py,yyy training minima correspond to solutions with large entropy of the examples,ly,yyy test examples size-normalized to I yx y, parameter distribution,which is beneficial to the general- and centered by center of mass in IsxIs fields)is avail- ization error. able at http]“F.2676L25h.Ltt.5 om"yInn“o52“mi7t. The influence of the training set size was measured by Figure 4 shows examples randomly picked from the test set.training the network with 15,yyy,3y,yyy,and Py,yyy exam- ples.The resulting training error and test error are shown B.Results in figure P.It is clear that,even with specialized architec- Several versions of EeNet-5 were trained on the regular tures such as EeNet-5,more training data would improve MNIST database.y iterations through the entire train-the accuracy. ing data were performed for each session.The values of To verify this hypothesis,we artificially generated more the global learning rate n(see-quation1 in Appendix C training examples by randomly distorting the original for a definition)was decreased using the following sched-training images.The increased training set was composed ulee y.yyy5 for the first two passes,y.yyyI for the next of the Py,yyy original patterns plus 54y,yyy instances of￾✂✁☎✄✝✆✟✞✠✄☛✡✌☞✎✍✟✏✒✑✓✏✂✏✂✏✎✔✖✕☛✄☎✗☛✏✙✘✛✚✙✏✂✁✢✜✤✣✥✣✧✦ ✜ ✝ ó✛å➈ê❨￾❶ì❛û➑û➀ï✒￾❶è✧ï✖ù❭å➄î➻ì❛é❼✂➉☞✇ï➊é☎ê✧ÿ☎ê❷✚➵ÿ✙ä✥ï✖å➄ÿ❙ï➊î➻æ✙û➀ì♦✘➈ï✖ï✖ê✒➌✠ó❨ç✙ø➑û➀ï➔þ✦✧✬✝❘➾ ó✛å➈ê✬￾➊ì➈û➀û➑ï★￾↔è✥ï✖ù✫å➄î➻ì❛é❼✂➓ç✙ø✠✂➈ç✦✝➠ê❺￾❿ç☎ì✐ì❛û❀ê✤è✧ÿ☎ù✂ï✖é✐è✥ê✖ð✬✧➉ä❿åró❨ø➀é❼✂➽ê✤ï✖é☎ê✧ø➟✝ ✡✙û➀ï✩￾❶ì➈é✥￾❶û➀ÿ☎ê✤ø➀ì➈é✎ê✝ëíä✥ì➈îòû➀ï✖å➈ä✧é☎ø➑é❼✂♣ï❯↔✂æ◆ï➊ä✥ø➑î➻ï➊é✐è❿ê❦ä✧ï★➍❛ÿ☎ø➑ä✥ï✖ê❀è✧ç☎å➄è❦è✧ç✙ï ä✥ï✖ê✧ÿ✙û➩è✎✡✎ï➤ø➀é☎ù✂ï✖æ✎ï✖é☎ù✂ï➊é✐è✛ì➄ë✝è✥ç✙ït￾❿ç✙ì➈ø✁￾❶ï➔ì➈ë✝è✧ä❿å➄ø➀é✙ø➀é❼✂❙ê✧ï❶è✛å➄é☎ù➽è✧ï❞ê④è å➄î➻ì❛é❼✂➻è✧ç✙ï➚￾❶ì❛î❭æ☎û➑ï➊è✧ï✒ê✧ï❶è➳ì➄ë➏ê✧å➈î➻æ✙û➑ï❞ê➊ð❨ã✛ç✙ï✖ä✧ï➊ëíì➈ä✥ï✌ø➩è➳ó➵å❛ê➔é✙ï★￾✹✝ ï✖ê✥ê✥å➄ä❘✘➞è✧ì➑✡✙ÿ✙ø➀û➀ù✶å➞é✙ï✖ó➘ù☎å✠è✥å✑✡☎å➈ê✧ï✛✡☛✘❭î❭ø✙↔✂ø➑é✗✂❙ñ✛➏✤þ✙ã ❁ ê➵ù✙å✠è❿å➈ê✧ï❶è❿ê➊ð þ✦✧✛✝✴➾➔￾➊ì➈é✐è✥å➈ø➑é☎ê ✙❆✺❼➌ ✙✫✑ ✔❺ù✂ø✙✂❛ø➩è✿ø➑î➓å✑✂➈ï✖ê➽ó❨ä✧ø➑è✤è✥ï➊é❭✡☛✘✩✙✻✘✻✘ ù✂ø➑ë●✝ ëíï➊ä✥ï➊é✐è➞ó❨ä✥ø➩è✥ï➊ä❿ê➊ð ➏➠é✢￾❶ì➈é✐è✥ä✥å❛ê④è➤è✧ì❖þ❼✧✛✝✝❜❼➌❇ó❨ç✙ï➊ä✥ï➵✡✙û➀ì☛￾❿ô✂ê➤ì➈ë❨ù☎å✠è✥å ëíä✥ì➈î▲ï✖å➎￾❿ç➓ó❨ä✧ø➑è✧ï✖ä✇å➄æ☎æ✎ï❞å➄ä✥ï✖ù❭ø➑é✢ê✤ï★➍❛ÿ☎ï➊é✗￾➊ï✑➌❛è✧ç✙ï➳ù✙å✠è❿å➞ø➀é✢þ✦✧✬✝❘➾➔ø✓ê ê❘￾❶ä❿å➄î➉✡☎û➑ï❞ù☛ð ✎ä✥ø➩è✥ï➊ä❨ø✓ù✂ï➊é✐è✥ø➩è✥ø➑ï❞ê✛ëíì➈ä➉þ✦✧✬✝✴➾➤å➈ä✧ï✌årú✠å➄ø➀û✓å❄✡✙û➀ï➳å➈é☎ù✿ó✇ï ÿ☎ê✧ï✖ù✿è✥ç✙ø➀ê♣ø➀é✂ëíì➈ä✥î➓å✠è✧ø➀ì➈é✿è✥ì✶ÿ✙é☎ê❘￾❶ä❿å➄î➑✡✙û➀ï➤è✧ç✙ï➞ó❨ä✥ø➑è✧ï➊ä❿ê✖ð ✎ï➞è✥ç✙ï➊é ê✧æ✙û➑ø➑è❯þ✦✧✬✝✴➾➏ø➑é➤è④ó➵ì❇✰✏￾❿ç✎å➄ä❿å✑￾↔è✥ï➊ä❿ê✟ó❨ä✧ø➑è✤è✥ï➊é✌✡☛✘♣è✧ç✙ï❷➞✎ä✥ê✤è ✑✫✙✻✘➵ó❨ä✧ø➑è✧ï✖ä✥ê ó➵ï➊é✐è➵ø➀é✐è✧ì➻ì➈ÿ☎ä➵é☎ï➊ó❍è✥ä✥å➈ø➑é✙ø➀é❼✂➻ê✤ï➊è✖ð➏ã✛ç✙ï➳ä✥ï➊î➓å➄ø➀é✙ø➀é❼✂❑✑ ✙❆✘✒ó❨ä✧ø➑è✧ï✖ä✥ê ó➵ï➊ä✥ï✢æ✙û✓å✑￾➊ï✖ù❑ø➑é ì➈ÿ☎ä❙è✥ï✖ê✤è➽ê✤ï➊è✖ð❑ã✛ç➇ÿ☎ê➻ó➵ï✿ç☎å➈ù❤è④ó✇ì➷ê✧ï❶è✥ê➻ó❨ø➑è✧ç é✙ï❞å➄ä✥û✙✘ ❜✻✘❼➌ ✘✻✘✗✘❖ï✄↔✙å➄î➻æ✙û➀ï✖ê➓ï❞å✑￾❿ç✝ð❲ã✛ç✙ï✫é✙ï➊ó▼è✥ä✥å➈ø➑é✙ø➀é❼✂ ê✧ï❶è➽ó✛å➈ê ￾❶ì❛î➻æ✙û➑ï➊è✧ï❞ù❑ó❨ø➑è✧ç➘ï✖é✙ì➈ÿ❼✂❛ç➘ï❯↔✙å➄î➻æ✙û➀ï✖ê❭ëíä✥ì➈î þ❼✧✛✝✝❜❼➌✛ê④è❿å➄ä✧è✧ø➀é❼✂ å✠è æ☎å➄è✤è✧ï✖ä✧é✁￾ ✘❼➌❛è✧ì❭î➻å➈ô➈ï➉å➞ëíÿ✙û➀û✟ê✧ï❶è✛ì➄ë★✓✗✘❼➌ ✘✻✘✗✘➳è✧ä❿å➄ø➀é✙ø➑é✗✂✒æ☎å➄è✤è✧ï✖ä✧é✎ê➊ð þ➇ø➀î➻ø➑û✓å➄ä✥û✙✘➎➌➄è✥ç✙ï➉é✙ï✖ó è✧ï✖ê✤è✇ê✧ï❶è❫ó✛å➈ê➜￾❶ì➈î➻æ✙û➀ï❶è✥ï✖ù➻ó❨ø➑è✧ç✶þ✦✧✬✝✝❜✌ï❯↔✙å➄î➚✝ æ✙û➀ï✖ê➞ê✤è✥å➈ä✤è✥ø➑é✗✂✺å➄è➞æ☎å✠è✧è✧ï✖ä✧é✂￾ ❜ ✙✦➌ ✘✻✘✗✘➽è✥ì✫î➓å➄ô➈ï➓å✿ëíÿ✙û➀û✇ê✧ï❶è➞ó❨ø➑è✧ç ✓✻✘✗➌ ✘✗✘✻✘✛è✥ï✖ê✤è❣æ☎å✠è✧è✧ï➊ä✥é☎ê✖ð❀➏➠é❙è✧ç✙ï✛ï✄↔➇æ◆ï➊ä✥ø➀î❭ï✖é✐è✥ê❦ù✂ï✖ê❘￾❶ä✥ø✠✡✎ï❞ù➞ç✙ï✖ä✧ï➎➌➄ó✇ï ì➈é☎û✙✘✢ÿ☎ê✤ï❞ù✺å➓ê✤ÿ❼✡✎ê✤ï➊è➔ì➄ë✔➾✽✘❼➌ ✘✻✘✗✘➞è✥ï✖ê✤è➉ø➀î➻å✑✂➈ï❞ê✌➪✮✙✦➌ ✘✻✘✗✘❙ëíä✧ì❛îPþ✦✧✬✝❘➾ å➄é✎ù ✙✦➌ ✘✻✘✗✘➳ëíä✧ì❛î✴þ✦✧✬✝✿❜❩➶✹➌☛✡✙ÿ✂è✛ó✇ï♣ÿ☎ê✧ï✖ù➓è✥ç✙ï➔ëíÿ☎û➑û ✓✗✘❼➌ ✘✻✘✻✘➳è✥ä✥å➈ø➑é☎ø➑é❼✂ ê✥å➄î➻æ✙û➀ï✖ê✖ð✿ã✛ç✙ï✶ä✧ï❞ê✤ÿ✙û➑è✧ø➀é❼✂➲ù✙å➄è✥å✑✡☎å➈ê✧ï➓ó➵å❛ê✌￾➊å➈û➑û➀ï✖ù è✥ç✙ï✶ö✫ì✂ù✂ø✙➞☎ï✖ù ñ✛➏✤þ✙ãt➌✙ì➈ä➔ö➲ñ✬➏✤þ✂ãt➌☎ù✙å➄è✥å❛ê✤ï➊è✖ð ã✛ç✙ï➓ì➈ä✥ø✙✂❛ø➑é✎å➄û❜✡✙û➀å➎￾❿ô❖å➄é✎ù❖ó❨ç✙ø➑è✧ï↕➪✡✙ø➀û➑ï✖ú➈ï➊û●➶➳ø➀î➻å✑✂➈ï❞ê♣ó➵ï➊ä✥ï➓ê✤ø✠➽➊ï é✙ì❛ä✧î➓å➄û➀ø✠➽➊ï✖ù✻è✧ì⑨➞✙è✫ø➀é❲å☞✑❆✘❄↔✤✑❆✘ æ☎ø➟↔✂ï➊ût✡◆ì✪↔✲ó❨ç✙ø➀û➑ï➷æ✙ä✥ï✖ê✧ï➊ä✥ú➇ø➑é✗✂ è✧ç☎ï➊ø➀ä➤å❛ê✤æ◆ï✒￾❶è➳ä❿å✠è✥ø➑ì✎ð➞ã✛ç✙ï❭ä✧ï❞ê✤ÿ✙û➑è✧ø➀é❼✂✢ø➑î➓å❄✂❛ï✖ê✞￾❶ì❛é❛è❿å➄ø➀é➔✂❛ä✧ï✒✘✿û➀ï➊ú❩✝ ï➊û✓ê➵å➈ê➏ä✥ï✖ê✧ÿ✙û➑è❫ì➄ë☛è✥ç✙ï♣å➈é✐è✧ø✙✝⑥å➈û➑ø✓å➈ê✧ø➑é✗✂➣➪íø➀î➻å✑✂➈ï➔ø➀é✐è✧ï✖ä✧æ◆ì➈û✓å✠è✥ø➑ì❛é✥➶❦è✥ï✒￾❿ç✦✝ é✙ø✁➍✐ÿ✙ï➷ÿ☎ê✤ï❞ù ✡☛✘❍è✥ç✙ï➷é✙ì➈ä✥î➓å➄û➀ø✙➽❞å✠è✧ø➀ì➈é✾å➄û✠✂➈ì➈ä✥ø➑è✧ç✙î✺ð ã✛ç✙ä✥ï➊ï➷ú➈ï✖ä❇✝ ê✧ø➑ì❛é☎ê➷ì➄ë✢è✧ç✙ï✻ù✙å➄è✥å✑✡☎å➈ê✧ï❑ó➵ï➊ä✥ï ÿ☎ê✤ï❞ù☛ð ➏➠é✹è✥ç✙ï ➞☎ä❿ê④è ú❛ï➊ä❿ê✤ø➀ì➈é✏➌ è✧ç☎ï❺ø➀î➓å❄✂➈ï❞ê✶ó➵ï➊ä✥ï➔￾➊ï➊é✐è✧ï✖ä✧ï❞ù❍ø➑é❲å ✑✻✺♦↔✤✑❆✺➷ø➀î➓å❄✂❛ï➔✡☛✘❭￾❶ì➈î➻æ✙ÿ✙è❇✝ ø➀é❼✂ è✧ç✙ï✆￾❶ï✖é✐è✧ï➊ä➻ì➈ë♣î➓å➈ê✥ê❭ì➄ë➉è✥ç✙ï✺æ✙ø✙↔➇ï✖û➀ê✒➌✇å➈é☎ù❤è✧ä❿å➄é☎ê✧û➀å➄è✧ø➀é❼✂❺è✧ç✙ï ø➀î➻å✑✂➈ï ê✧ì❍å➈ê✺è✥ì❍æ✎ì✐ê✤ø➑è✧ø➀ì➈é❲è✧ç☎ø➀ê✫æ◆ì➈ø➀é✐è❺å✠è✫è✥ç✙ï✢￾❶ï✖é✐è✧ï➊ä❖ì➄ë❭è✧ç✙ï ✑❆✺❄↔✤✑❆✺➛➞☎ï➊û✓ù☛ð✖➏➠é✻ê✤ì❛î➻ï✫ø➑é☎ê✤è✥å➈é✗￾❶ï❞ê✄➌➵è✥ç✙ø➀ê✳✑❆✺❄↔✑✻✺➛➞☎ï➊û✓ù➘ó➵å❛ê➓ï❯↔☛✝ è✧ï✖é☎ù✂ï❞ù è✧ì ❜✵✑✪↔❜ ✑✢ó❨ø➑è✧ç①✡☎å➎￾❿ô❩✂❛ä✧ì❛ÿ✙é☎ù❺æ✙ø✙↔➇ï✖û➀ê✖ð✢ã✛ç☎ø➀ê✒ú➈ï➊ä❿ê✧ø➑ì❛é❺ì➈ë è✧ç☎ï➲ù✙å✠è❿å❄✡☎å❛ê✤ï✢ó❨ø➑û➀û✩✡✎ï✫ä✥ï❶ëíï✖ä✧ä✥ï✖ù è✧ì å➈ê❙è✥ç✙ï ➡❺➳✿✥✡✔✲✙➢❄➡❙ù✙å➄è✥å✑✡☎å➈ê✧ï➈ð ➏➠é❑è✧ç✙ï✫ê✧ï✒￾❶ì❛é☎ù ú❛ï➊ä❿ê✤ø➀ì➈é❤ì➄ë➉è✥ç✙ï✫ù✙å✠è❿å❄✡☎å❛ê✤ï➎➌❣è✧ç☎ï✫￾❿ç✎å➄ä❿å✑￾↔è✥ï➊ä❙ø➑î➚✝ å❄✂❛ï✖ê✇ó✇ï✖ä✧ï➳ù✂ï✖ê✧û✓å➄é✐è✧ï❞ù➽å➄é☎ù➙￾❶ä✥ì➈æ✙æ◆ï✖ù✶ù✂ì✠ó❨é➽è✥ì❑✑✻✘♦↔✤✑❆✘✌æ☎ø➟↔✂ï➊û✓ê✇ø➑î➚✝ å❄✂❛ï✖ê✖ð✇ã✛ç✙ï➞ù✙ï✖ê✧û➀å➈é❛è✥ø➑é✗✂➣￾❶ì➈î➻æ✙ÿ✙è✧ï✖ê➔è✧ç✙ï❙ê✤ï★￾❶ì➈é✎ù✶î➻ì➈î➻ï✖é❛è❿ê➔ì➈ë❯ø➀é✦✝ ï➊ä✧è✧ø✓å➻ì➄ë❦è✥ç✙ï✒æ✙ø✙↔✂ï➊û✓ê➉➪✻￾❶ì➈ÿ☎é❛è✥ø➑é✗✂➽å➻ëíì➈ä✥ï✄✂❛ä✧ì❛ÿ✙é☎ù✢æ✙ø➟↔✂ï✖û❇å➈ê➓➾✒å➄é☎ù✫å ✡☎å➎￾❿ô❩✂❛ä✧ì❛ÿ✙é☎ù✺æ✙ø✙↔✂ï➊û➏å❛ê✤✘❩➶✹➌✝å➄é✎ù❖ê✧ç✙ï✖å➈ä✥ê➉è✧ç✙ï❭ø➀î➻å✑✂➈ï➚✡☛✘✫ç✙ì➈ä✥ø✙➽✖ì➈é✦✝ è✥å➈û➑û✠✘ ê✤ç☎ø➩ë➺è✥ø➑é❼✂❖è✧ç✙ï✿û➀ø➑é✙ï❞ê❙ê✧ì✫è✥ç☎å✠è❙è✧ç✙ï✿æ✙ä✥ø➑é✗￾➊ø➑æ✎å➄û✇å❄↔✂ø➀ê✒ø➀ê❙ú➈ï✖ä✤è✥ø➟✝ ￾➊å➈ûüð➏ã✛ç☎ø➀ê✛ú❛ï➊ä❿ê✤ø➀ì➈é✢ì➄ë❯è✧ç✙ï➞ù✙å➄è✥å✑✡☎å➈ê✧ï♣ó❨ø➀û➀û✏✡✎ï✌ä✥ï❶ëíï✖ä✧ä✥ï✖ù➽è✧ì➽å❛ê➵è✧ç✙ï ✪✑➳❯➩▼✲✙➢♦➨✥➺❖➳✱✪✶ù✙å✠è❿å❄✡☎å❛ê✤ï❛ð ➏➠é➷è✧ç☎ï➓è✧ç✙ø➀ä❿ù➷ú➈ï➊ä❿ê✧ø➑ì❛é❺ì➈ë➵è✥ç✙ï✶ù✙å➄è✥å✑✡☎å➈ê✧ï✑➌ ÿ☎ê✧ï✖ù❺ø➑é ê✧ì➈î➻ï❭ï✖å➄ä✥û✠✘✫ï❯↔✂æ✎ï✖ä✧ø➀î➻ï➊é✐è✥ê✒➌☛è✥ç✙ï➻ø➑î➓å❄✂❛ï✖ê➳ó➵ï➊ä✥ï❭ä✥ï✖ù✙ÿ✗￾❶ï❞ù è✧ì✟➾✒✓♦↔❢➾✽✓❑æ✙ø✙↔➇ï✖û➀ê✖ð ã✛ç✙ï➷ä✧ï✒✂➈ÿ✙û✓å➄ä✫ù✙å➄è✥å✑✡☎å➈ê✧ï⑨➪✡✓✻✘✗➌ ✘✗✘✻✘ è✥ä✥å➈ø➑é☎ø➑é❼✂ ï❯↔✙å➈î❭æ☎û➑ï❞ê✄➌✎➾✽✘✗➌ ✘✗✘✻✘✶è✧ï✖ê✤è✒ï✄↔✂å➈î➻æ✙û➑ï❞ê➞ê✧ø✙➽✖ï❯✝⑥é✙ì➈ä✥î➓å➄û➀ø✙➽✖ï✖ù❖è✧ì ✑❆✘❄↔✤✑❆✘❼➌ å➄é✎ù⑨￾➊ï➊é✐è✧ï✖ä✧ï❞ù➹✡☛✘⑨￾❶ï➊é✐è✥ï➊ä➽ì➈ë➳î➓å➈ê✥ê➻ø➀é☞✑✻✺♦↔✤✑❆✺➔➞☎ï✖û➀ù✙ê✴➶➻ø✓ê➓årú✠å➄ø➀û➟✝ å❄✡☎û➑ï❫å➄è☎✄✝✆✞✆✞✟✡✠☞☛✌☛✎✍✌✍✌✍✡✏✒✑✝✓✕✔✖✓✌✗✘✑✕✙✚✄✡✏✒✗✘✆✞✆✛✏✜✙✣✢✚✤✥☛✧✦★✝✗✖✩✞✩✕☛✞✢✝✙✎✑✕☛✪✤✫✩✭✬✞✔✎✆✎ð ✜❯ø✙✂❛ÿ✙ä✥ï ❝➉ê✧ç✙ì✠ó➔ê✝ï✄↔✙å➄î➻æ✙û➀ï✖ê✝ä❿å➄é✎ù✂ì➈î➻û✠✘♣æ✙ø✁￾❿ô➈ï❞ù➤ëíä✥ì➈î✾è✧ç✙ï✇è✧ï❞ê④è❦ê✤ï➊è✖ð ✬✛ ✁④➳✹➩✒✡✔✲➂➺✻➩ þ➇ï➊ú❛ï➊ä❿å➄û❯ú➈ï➊ä❿ê✧ø➑ì❛é☎ê➔ì➈ë✄✗✝ï❞ñ➔ï❶è❺✝✝✙➽ó✇ï✖ä✧ï✒è✧ä❿å➄ø➀é✙ï✖ù❖ì➈é❖è✧ç✙ï❭ä✧ï✒✂➈ÿ✙û✓å➄ä ö➲ñ✬➏✤þ✂ã ù✙å✠è❿å❄✡☎å❛ê✤ï❛ð◆✑✻✘✺ø➩è✥ï➊ä❿å✠è✥ø➑ì❛é☎ê➤è✧ç☎ä✧ì❛ÿ❼✂➈ç➷è✥ç✙ï➽ï➊é✐è✥ø➑ä✥ï➓è✧ä❿å➄ø➀é✦✝ ø➀é❼✂ ù☎å✠è✥å❖ó✇ï✖ä✧ï✢æ✎ï✖ä✤ëíì❛ä✧î➻ï❞ù ëíì➈ä❭ï✖å➎￾❿ç❑ê✧ï✖ê✥ê✤ø➀ì➈é❀ð➷ã✛ç☎ï✢ú✠å➄û➀ÿ✙ï❞ê✒ì➈ë è✧ç☎ï✞✂❛û➑ì➎✡☎å➄û✟û➀ï✖å➈ä✧é✙ø➀é❼✂❙ä✥å➄è✧ï✯✮➔➪⑨ê✧ï➊ï ✭➜➍✐ÿ☎å➄è✧ø➀ì➈é◆✑✦➾➳ø➑é✫✕➔æ✙æ◆ï➊é✎ù✂ø➟↔✆☞ ëíì➈ä❙å✫ù✂ï❯➞☎é☎ø➩è✥ø➑ì❛é✥➶➤ó✛å➈ê➞ù✂ï★￾❶ä✥ï✖å❛ê✤ï❞ù❖ÿ☎ê✧ø➀é❼✂✺è✧ç✙ï➽ëíì➈û➀û➑ì✠ó❨ø➀é❼✂✫ê❺￾❿ç☎ï✖ù☛✝ ÿ✙û➀ï✻✰✶✘✙ð ✘✻✘✗✘ ✙❖ëíì➈ä✶è✧ç✙ï✆➞✎ä✥ê✤è➽è④ó➵ì æ☎å➈ê✥ê✤ï❞ê✄➌ ✘☎ð ✘✗✘✻✘ ✑❖ëíì❛ä➽è✧ç☎ï➲é✙ï❯↔➇è ✁✗✿▲❍✪❦✱✰✪❦➙❁✒✿▲❵❅✰r❑●❈✪✷✹✸✶❋✛✱✴❴▲✿▲❵❅✰❅❉✬✰☎★✱✴❋✩❃✪❴▲✰❅✺❢⑥✠✸✻✷✹❋①✵✶✯✪✰➜❸✌❤❀❊ ❁✒✮✆❉♦✱❘✵✶✱✴◗♦✱✴✺✶✰✹❦ è✧ç☎ä✧ï✖ï✑➌ ✘✙ð ✘✻✘✻✘✗➾➽ëíì❛ä➓è✧ç✙ï✫é☎ï❯↔➇è➻è✧ç✙ä✥ï➊ï➎➌ ✘☎ð ✘✗✘✻✘✻✘✵✙✺ëíì❛ä➓è✧ç✙ï✫é☎ï❯↔➇è ❝✗➌ å➄é✎ù✚✘✙ð ✘✻✘✗✘✻✘❼➾➵è✥ç✙ï➊ä✥ï✖å➄ë➺è✧ï➊ä❞ð❷✚➵ï❶ëíì➈ä✥ï➔ï❞å✑￾❿ç➓ø➑è✧ï➊ä❿å✠è✥ø➑ì❛é✏➌❛è✧ç✙ï➤ù✂ø✓å❄✂➈ì❛é☎å➄û õ➔ï❞ê✧ê✧ø✓å➄é➽å➄æ☎æ✙ä✧ì✪↔✂ø➀î➓å✠è✧ø➀ì➈é➻ó✛å➈ê❫ä✧ï✖ï➊ú✠å➄û➀ÿ☎å✠è✥ï✖ù➻ì❛é ✙❆✘✗✘✌ê✧å➈î❭æ☎û➑ï❞ê✄➌➇å➈ê ù✂ï❞ê❺￾➊ä✧ø✠✡✎ï❞ù✫ø➀é➔✕➔æ✙æ◆ï➊é✎ù✂ø➟↔➒☞❲å➈é☎ù✫ô❛ï➊æ✂è④➞❼↔✂ï✖ù➲ù✂ÿ☎ä✧ø➀é❼✂➽è✥ç✙ï❭ï➊é✐è✧ø➀ä✧ï ø➑è✧ï➊ä❿å✠è✥ø➑ì❛é✝ð✛ã✛ç✙ï➞æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä✳✲ ó✛å➈ê❨ê✧ï❶è➉è✧ì✙✘☎ð ✘✵✑✂ð✇ã✛ç☎ï➞ä✧ï❞ê✤ÿ☎û➩è✥ø➑é❼✂ ï❯➘✟ï✒￾❶è✧ø➀ú➈ï➔û➀ï✖å➈ä✧é☎ø➑é❼✂✌ä❿å✠è✥ï✖ê➏ù✙ÿ✙ä✧ø➀é❼✂✌è✥ç✙ï✩➞☎ä❿ê✤è❫æ☎å➈ê✥ê➏ú✠å➈ä✧ø➀ï✖ù➚✡◆ï❶è④ó➵ï➊ï➊é å➄æ☎æ✙ä✧ì✪↔✂ø➀î➓å✠è✧ï✖û✙✘✜✔✵✴➛➾✒✘ ✴ ￾ å➈é☎ù ✘ ❭ ✘❼➾✽✓❭ì✠ú❛ï➊ä➵è✧ç✙ï➞ê✧ï❶è♣ì➄ë❦æ☎å➄ä❿å➄î➻ï❯✝ è✧ï✖ä✥ê✖ð✒ã✛ç✙ï❭è✥ï✖ê✤è➤ï✖ä✧ä✥ì➈ä➳ä❿å✠è✧ï➻ê✤è✥å❄✡☎ø➑û➀ø✙➽✖ï✖ê➤å✠ë➺è✥ï➊ä✌å➄ä✥ì➈ÿ☎é☎ù✢➾✒✘➽æ☎å❛ê✧ê✧ï✖ê è✧ç☎ä✧ì❛ÿ❼✂➈ç❺è✧ç✙ï➻è✥ä✥å➈ø➑é☎ø➑é❼✂✺ê✧ï❶è✒å✠è✛✘☎ð ❀✵✙✘✶✶ð➓ã✛ç✙ï➻ï➊ä✥ä✧ì❛ä➳ä❿å✠è✥ï❙ì❛é è✧ç✙ï è✧ä❿å➄ø➀é✙ø➀é❼✂✺ê✤ï➊è➤ä✥ï✖å➎￾❿ç✙ï✖ê ✘✙ð ❜ ✙✞✶På✠ë➺è✧ï✖ä➝➾✽❀✢æ☎å➈ê✥ê✤ï❞ê➊ð❙ö➲å➄é☛✘➲å➄ÿ✙è✧ç✙ì❛ä✥ê ç☎årú❛ï➔ä✧ï✖æ✎ì❛ä✤è✥ï✖ù➻ì➎✡☎ê✤ï✖ä✧ú➇ø➀é❼✂✌è✥ç✙ï✞￾➊ì➈î➻î➻ì➈é➓æ✙ç☎ï➊é✙ì❛î❭ï✖é✙ì➈é✶ì➄ë✝ì✠ú➈ï✖ä❇✝ è✧ä❿å➄ø➀é✙ø➀é❼✂✺ó❨ç✙ï➊é è✥ä✥å➈ø➑é✙ø➀é❼✂✫é✙ï✖ÿ✙ä❿å➄û❣é✙ï➊è④ó✇ì❛ä✧ô✂ê➳ì➈ä➞ì➈è✧ç✙ï✖ä➞å➈ù✙å➈æ✂è✧ø➀ú➈ï å➄û✠✂➈ì❛ä✧ø➑è✧ç☎î➻ê❙ì➈é ú✠å➄ä✥ø➑ì❛ÿ☎ê✒è✥å➈ê✧ô✂ê➊ð ✎ç✙ï➊é ì✠ú➈ï✖ä❇✝♠è✧ä❿å➄ø➀é✙ø➀é❼✂➲ì✦￾✄￾➊ÿ✙ä❿ê✄➌ è✧ç☎ï✌è✧ä❿å➄ø➀é✙ø➀é❼✂➓ï➊ä✥ä✧ì❛ä❨ô➈ï✖ï➊æ☎ê❨ù✂ï★￾❶ä✥ï✖å❛ê✤ø➀é❼✂➻ì✠ú➈ï✖ä✛è✧ø➀î❭ï➎➌✥✡☎ÿ✂è➔è✧ç☎ï✌è✧ï❞ê④è ï➊ä✥ä✥ì➈ä✛✂❛ì✐ï❞ê➔è✥ç✙ä✥ì➈ÿ❼✂❛ç❖å➽î➻ø➀é✙ø➑î❙ÿ✙î å➄é✎ù➲ê④è❿å➄ä✧è✥ê➉ø➑é✗￾➊ä✧ï❞å➈ê✧ø➑é✗✂✶å✠ë➺è✥ï➊ä å ￾➊ï➊ä✧è✥å➈ø➑é✫é➇ÿ✙î➑✡✎ï✖ä♣ì➈ë➏ø➩è✥ï➊ä❿å✠è✧ø➀ì➈é✎ê➊ð ✎ç☎ø➑û➀ï➞è✥ç✙ø➀ê➳æ✙ç☎ï➊é✙ì❛î❭ï✖é✙ì➈é✫ø✓ê ú➈ï✖ä❺✘➝￾❶ì❛î➻î❭ì❛é✏➌✐ø➩è➵ó➵å❛ê➏é✙ì➈è❫ì✑✡☎ê✧ï➊ä✥ú➈ï❞ù➻ø➑é✶ì➈ÿ✙ä✎￾➊å➈ê✧ï➉å❛ê❣è✧ç☎ï➉û➀ï✖å➄ä✥é✦✝ ø➀é❼✂➐￾➊ÿ✙ä✥ú➈ï✖ê♣ø➀é↕➞✗✂❛ÿ✙ä✧ï❑✙✶ê✧ç✙ì✠ó✌ð➓✕➶æ✎ì✐ê✧ê✧ø✠✡✙û➑ï❭ä✥ï✖å➈ê✧ì➈é✫ø✓ê♣è✧ç☎å➄è➤è✧ç✙ï û➀ï✖å➄ä✥é✙ø➀é❼✂➞ä❿å✠è✥ï➉ó✛å➈ê➏ô❛ï➊æ✂è✛ä✥ï➊û✓å✠è✧ø➀ú➈ï✖û✙✘❭û✓å➄ä❘✂➈ï➈ð❦ã✛ç✙ï♣ï❯➘✟ï✒￾↔è✛ì➄ë☛è✥ç✙ø✓ê✇ø✓ê è✧ç✎å✠è➞è✥ç✙ï➽ó➵ï➊ø✠✂➈ç✐è✥ê➤é✙ï✖ú➈ï✖ä➞ê✤ï➊è✤è✧û➀ï✶ù✂ì✠ó❨é➷ø➀é➷è✧ç✙ï✶û➑ì✦￾➊å➈û❣î➻ø➑é✙ø➀î✒ÿ☎î ✡✙ÿ✂è➓ô❛ï➊ï➊æ❤ì❛ê❘￾❶ø➀û➑û✓å✠è✥ø➑é❼✂❺ä✥å➈é☎ù✂ì❛î❭û✠✘➈ð✢✚➵ï★￾➊å➄ÿ✎ê✤ï✢ì➄ë➔è✥ç✙ì❛ê✧ï✚✾☎ÿ✥￾↔è✧ÿ✎å♦✝ è✧ø➀ì➈é✎ê✄➌✠è✥ç✙ï➔årú➈ï✖ä✥å✑✂➈ï✎￾❶ì❛ê✤è❣ó❨ø➑û➀û❼✡◆ï❨û➑ì✠ó➵ï➊ä❦ø➀é❭åt✡☎ä✧ì✐å➈ù✂ï✖ä❇î➻ø➀é✙ø➑î❙ÿ✙î✺ð ã✛ç✙ï✖ä✧ï➊ëíì➈ä✥ï✑➌✟ê④è✥ì☛￾❿ç✎å➈ê✤è✧ø✁￾✌✂➈ä❿å➈ù✂ø➀ï➊é✐è➉ó❨ø➀û➀û❇ç☎årú❛ï✒å✶ê✧ø➀î❭ø➀û✓å➄ä➉ï✄➘◆ï★￾↔è✌å➈ê å➤ä✥ï✄✂➈ÿ☎û➀å➈ä✧ø✠➽✖å➄è✧ø➀ì➈é➞è✥ï➊ä✥îòè✥ç☎å✠è❣ë⑨årú❛ì➈ä❿ê❳✡☎ä✧ì✐å➈ù✂ï✖ä❣î❭ø➀é✙ø➀î➓å✙ð❨✚✇ä✥ì❛å❛ù✂ï➊ä î➻ø➑é☎ø➑î➓å✫￾❶ì❛ä✧ä✥ï✖ê✧æ✎ì❛é☎ù✫è✥ì✫ê✤ì❛û➑ÿ✂è✥ø➑ì❛é☎ê➤ó❨ø➑è✧ç➷û➀å➈ä❺✂❛ï✒ï✖é❛è✥ä✧ì❛æ☛✘✫ì➄ë➵è✧ç✙ï æ☎å➈ä✥å➈î❭ï➊è✧ï✖ä♣ù✂ø✓ê④è✥ä✧ø✠✡✙ÿ✂è✥ø➑ì❛é✏➌☛ó❨ç✙ø✁￾❿ç➲ø✓ê④✡◆ï➊é☎ï❯➞✥￾➊ø➀å➈û❀è✥ì✶è✥ç✙ï➑✂❛ï➊é✙ï✖ä✥å➈û➟✝ ø✠➽✖å✠è✥ø➑ì❛é✢ï✖ä✧ä✥ì➈ä❞ð ã✛ç✙ï➽ø➀é✾☎ÿ✙ï✖é✗￾❶ï✢ì➄ë✛è✧ç✙ï➽è✧ä❿å➄ø➀é✙ø➑é✗✂➲ê✤ï➊è❙ê✤ø✠➽➊ï✶ó➵å❛ê✌î➻ï✖å➈ê✧ÿ✙ä✥ï✖ù➒✡☛✘ è✧ä❿å➄ø➀é✙ø➀é❼✂➔è✥ç✙ï✛é✙ï❶è④ó➵ì➈ä✥ô➳ó❨ø➩è✥ç ➾ ✙❼➌ ✘✗✘✻✘✗➌ ❜✗✘❼➌ ✘✻✘✻✘✗➌✠å➄é☎ù✛✓✗✘❼➌ ✘✻✘✗✘❨ï❯↔✙å➄î➚✝ æ✙û➀ï✖ê✖ð➏ã✛ç✙ï➤ä✧ï❞ê✤ÿ☎û➩è✥ø➑é❼✂❙è✧ä❿å➄ø➀é✙ø➀é❼✂❭ï➊ä✥ä✧ì❛ä➵å➈é☎ù➽è✥ï✖ê✤è❨ï➊ä✥ä✧ì❛ä➵å➈ä✧ï➤ê✤ç☎ì✠ó❨é ø➀é➙➞✥✂➈ÿ✙ä✥ï✛✓✙ð❹➏⑥è➔ø✓ê✛￾➊û➑ï❞å➄ä✛è✧ç✎å✠è✒➌✎ï➊ú❛ï➊é✿ó❨ø➩è✥ç➲ê✤æ◆ï✒￾➊ø➀å➈û➑ø✠➽➊ï❞ù✢å➈ä❘￾❿ç✙ø➑è✧ï★￾✹✝ è✧ÿ☎ä✧ï❞ê➳ê✧ÿ✗￾❿ç➷å➈ê✒✗✝ï❞ñ➔ï➊è❇✝ ✙✦➌☛î➻ì➈ä✥ï✒è✥ä✥å➈ø➑é☎ø➑é❼✂✺ù✙å➄è✥å✢ó✇ì❛ÿ✙û➀ù❖ø➑î➻æ✙ä✥ì✠ú➈ï è✧ç☎ï➞å✑￾✄￾➊ÿ✙ä❿å✑￾❯✘❛ð ã❀ì➓ú❛ï➊ä✥ø➩ë➭✘✶è✧ç✙ø✓ê➔ç☛✘➇æ✎ì➈è✧ç✙ï❞ê✤ø✓ê✒➌☎ó➵ï➞å➄ä✧è✧ø✙➞✥￾❶ø✓å➄û➀û✙✘ ✂➈ï➊é☎ï➊ä❿å✠è✧ï❞ù✿î❭ì❛ä✧ï è✧ä❿å➄ø➀é✙ø➀é❼✂ ï✄↔✂å➈î➻æ✙û➑ï❞ê❭✡☛✘Pä❿å➄é✎ù✂ì➈î➻û✠✘Pù✂ø✓ê④è✥ì➈ä✧è✧ø➀é❼✂ è✥ç✙ï✹ì❛ä✧ø✠✂➈ø➀é☎å➄û è✧ä❿å➄ø➀é✙ø➀é❼✂➓ø➀î➻å✑✂➈ï❞ê➊ð❫ã✛ç☎ï✌ø➑é✗￾➊ä✧ï❞å➈ê✧ï✖ù✶è✧ä❿å➄ø➀é✙ø➀é❼✂➽ê✤ï➊è➔ó➵å❛ê✛￾❶ì❛î➻æ✎ì✐ê✤ï❞ù ì➄ë➤è✥ç✙ï✦✓✻✘✗➌ ✘✗✘✻✘ ì➈ä✥ø✠✂➈ø➀é☎å➄û❨æ☎å➄è✤è✥ï➊ä✥é☎ê➽æ✙û➀ÿ☎ê✳✙❝✗✘✗➌ ✘✗✘✻✘❺ø➑é✎ê④è❿å➄é✗￾➊ï✖ê➓ì➈ë