2012年“TI”杯四川省電子設(shè)計(jì)競(jìng)賽聲音定位系統(tǒng)（D題）競(jìng)賽選題： 聲音定位系統(tǒng)（D題）學(xué) 校： 西南石油大學(xué) 參賽隊(duì)員：楊 杰 劉德雄 康 敏摘 要本設(shè)計(jì)采用TI公司生產(chǎn)的超低功耗單片機(jī)MSP430G2452和G2553分別作為定位系統(tǒng)的聲源產(chǎn)生模塊和信息處理模塊，實(shí)現(xiàn)了聲音信號(hào)的發(fā)生、信號(hào)收集處理和屏幕顯示以及語(yǔ)音提示等功能。該設(shè)計(jì)采用2節(jié)家用1.5V電池供電，實(shí)現(xiàn)了低功耗狀況下的聲音定位系。聲源接收單元信號(hào)反應(yīng)靈敏，能較準(zhǔn)確的得到信號(hào)并及時(shí)傳送到信號(hào)處理單元。以MSP430為主的Launchpad也符合了低功耗的標(biāo)準(zhǔn)，并且可以實(shí)現(xiàn)信號(hào)的運(yùn)算處理以及控制LCD液晶屏幕顯示測(cè)試數(shù)據(jù)。在定位算法上采用的是歸一正方形算法。通過(guò)調(diào)試修正以后，能實(shí)現(xiàn)基本的聲源定位并顯示。關(guān)鍵詞：聲音定位 低功耗 MSP430目 錄一引言31.1主要任務(wù)31.2設(shè)計(jì)要求4二.方案設(shè)計(jì)與論證42.1方案對(duì)比42.1.1 聲源模塊52.1.2 接收模塊放大芯片52.1.3 單片機(jī)MCU62.1.4 顯示模塊72.1.5 定位算法選擇8三硬件電路設(shè)計(jì)93.1 系統(tǒng)框圖93.2聲響模塊103.3 從單片機(jī)最小系統(tǒng)103.4聲音接收模塊113.5信號(hào)處理模塊123.6 語(yǔ)音模塊12四. 軟件設(shè)計(jì)124.1 軟件流程圖13五.測(cè)試結(jié)果與分析145.1 測(cè)試方法與儀器155.2 測(cè)試數(shù)據(jù)155.3 測(cè)試結(jié)果分析155.4 測(cè)試結(jié)果15參考文獻(xiàn)16附錄一：17附錄二：18附錄三：19一、引言 1.1主要任務(wù)設(shè)計(jì)一套聲音定位系統(tǒng)。在一塊不大于1m2的平板上貼一張500mm350mm的坐標(biāo)紙，在其四角外側(cè)分別固定安裝一個(gè)聲音接收模塊，聲音接收模塊通過(guò)導(dǎo)線(xiàn)將聲音信號(hào)傳輸?shù)叫畔⑻幚砟K，聲音定位系統(tǒng)根據(jù)聲響模塊通過(guò)空氣傳播到各聲音接收模塊的聲音信號(hào)，判定聲響模塊所在的位置坐標(biāo)。系統(tǒng)結(jié)構(gòu)示意圖如圖1所示。圖1 聲音定位系統(tǒng)結(jié)構(gòu)示意圖1.2設(shè)計(jì)要求【1】. 基本要求(1) 設(shè)計(jì)制作一個(gè)聲響模塊，含信號(hào)產(chǎn)生電路、放大電路和微型揚(yáng)聲器等，每按鍵一次發(fā)聲一次，聲音信號(hào)的基波頻率為500Hz左右，聲音持續(xù)時(shí)間約為1s。要求聲響模塊采用3V以下電池供電，功耗不大于200mW。(2) 設(shè)計(jì)制作四路聲音接收模塊，由麥克風(fēng)、放大電路等組成，并分別與信息處理模塊相連接，以便將頻率為500Hz左右的信號(hào)傳送至信息處理模塊。(3) 設(shè)計(jì)制作一個(gè)信息處理模塊，要求該模塊能根據(jù)從聲音接收模塊傳來(lái)的信號(hào)判斷聲響模塊所在位置的x、y坐標(biāo)，并以數(shù)字形式顯示x、y坐標(biāo)值，位置坐標(biāo)值誤差的絕對(duì)值不大于30mm?！?】. 發(fā)揮部分(1) 改善接收信號(hào)的放大電路性能，改進(jìn)算法，進(jìn)一步提高定位精度。(2) 控制聲響模塊以不間斷的連續(xù)周期波的形式發(fā)出聲音信號(hào)，其基波頻率為500Hz左右。當(dāng)聲響模塊在坐標(biāo)紙上移動(dòng)時(shí)，聲音定位系統(tǒng)能連續(xù)跟蹤顯示聲響模塊的x、y坐標(biāo)值，隨機(jī)停止聲響模塊的移動(dòng)，能立即穩(wěn)定地顯示聲響模塊的x、y坐標(biāo)值，誤差的絕對(duì)值不大于10mm。(3) 具有顯示聲響模塊移動(dòng)軌跡的功能。當(dāng)聲響模塊在坐標(biāo)紙上按指定路徑移動(dòng)時(shí)，液晶顯示屏能動(dòng)態(tài)顯示聲響模塊移動(dòng)的軌跡，顯示的軌跡與聲響模塊移動(dòng)的路徑一致。(4) 其它。二 方案設(shè)計(jì)與論證2.1方案對(duì)比 本設(shè)計(jì)分以下幾個(gè)模塊組成：聲響模塊、聲音接受模塊、信號(hào)處理模塊。現(xiàn)對(duì)模塊的選用方案進(jìn)行論證。2.1.1 聲源模塊設(shè)計(jì)要求聲響模塊采用3V以下電池供電，功耗不大于200mW。方案一：有源蜂鳴器蜂鳴器是一種一體化結(jié)構(gòu)的電子訊響器，采用直流電壓供電，廣泛應(yīng)用于計(jì)算機(jī)、打印機(jī)、復(fù)印機(jī)、報(bào)警器、電子玩具、汽車(chē)電子設(shè)備、電話(huà)機(jī)、定時(shí)器等電子產(chǎn)品中作發(fā)聲器件。方案二：無(wú)源蜂鳴器有源和無(wú)源的區(qū)別：這里的“源”不是指電源。而是指震蕩源。也就是說(shuō)，有源蜂鳴器內(nèi)部帶震蕩源，所以只要一通電就會(huì)叫。而無(wú)源內(nèi)部不帶震蕩源，所以如果用直流信號(hào)無(wú)法令其鳴叫。必須用2K5K的方波去驅(qū)動(dòng)它。有源蜂鳴器往往比無(wú)源的貴，就是因?yàn)槔锩娑鄠€(gè)震蕩電路。方案三：喇叭 8歐0.5瓦喇叭價(jià)格實(shí)惠，聲音響亮，聲音純度較高，并且完全滿(mǎn)足本次設(shè)計(jì)的需求，故本次采用的是喇叭作為發(fā)聲源。綜上所述，選取便宜可控的喇叭更符合設(shè)計(jì)需要。2.1.2 接收模塊放大芯片方案一：LM358LM358 內(nèi)部包括有兩個(gè)獨(dú)立的、高增益、內(nèi)部頻率補(bǔ)償?shù)碾p運(yùn)算放大器，適合于電源電壓范圍很寬的單電源使用，也適用于雙電源工作模式，在推薦的工作條件下，電源電流與電源電壓無(wú)關(guān)。它的使用范圍包括傳感放大器、直流增益模塊和其他所有可用單電源供電的使用運(yùn)算放大器的場(chǎng)合。圖2 lm358結(jié)構(gòu)圖方案二：LM368LM386是美國(guó)國(guó)家半導(dǎo)體公司生產(chǎn)的音頻功率放大器，主要應(yīng)用于低電壓消費(fèi)類(lèi)產(chǎn)品。為使外圍元件最少，電壓增益內(nèi)置為20。但在1腳和8腳之間增加一只外接電阻和電容，便可將電壓增益調(diào)為任意值，直至 200。輸入端以地為參考，同時(shí)輸出端被自動(dòng)偏置到電源電壓的一半，在6V電源電壓下，它的靜態(tài)功耗僅為24mW，使得LM386特別適用于電池供電的場(chǎng)合。圖3 lm386管腳圖方案三：LM393LM393是高增益,寬頻帶器件，象大多數(shù)比較器一樣，如果輸出端到輸入端有寄生電容而產(chǎn)生耦合，則很容易產(chǎn)生振蕩。這種現(xiàn)象僅僅出現(xiàn)在當(dāng)比較器改變狀態(tài)時(shí)，輸出電壓過(guò)渡的間隙，電源加旁路濾波并不能解決這個(gè)問(wèn)題，標(biāo)準(zhǔn)PC板的設(shè)計(jì)對(duì)減小輸入輸出寄生電容耦合是有助的。減小輸入電阻至小于10K將減小反饋信號(hào)，而且增加甚至很小的正反饋量(滯回1.010mV)能導(dǎo)致快速轉(zhuǎn)換,使得不可能產(chǎn)生由于寄生電容引起的振蕩，除非利用滯后，否則直接插入IC 并在引腳上加上電阻將引起輸入輸出在很短的轉(zhuǎn)換周期內(nèi)振蕩，如果輸入信號(hào)時(shí)脈沖波形，并且上升和下降時(shí)間相當(dāng)快，則滯回將不需要。圖4 lm393管腳圖由于接收信號(hào)微弱，要得到更精準(zhǔn)的聲源信號(hào)，選取了工作電源范圍更寬、輸入失調(diào)電壓更小的LM393。2.1.3 單片機(jī)MCU方案一：MSP430MSP430系列單片機(jī)是美國(guó)德州儀器公司（TI）1996年開(kāi)始推向市場(chǎng)的一種16位超低功耗、具有精簡(jiǎn)指令集的混合信號(hào)處理器。稱(chēng)之為混合信號(hào)處理器，是由于其針對(duì)實(shí)際應(yīng)用需求，將多個(gè)不同功能的模擬電路、數(shù)字電路模塊和微處理器集成在一個(gè)芯片上，以提供“單片機(jī)”解決方案。該系列單片機(jī)多應(yīng)用于需要電池供電的便攜式儀器儀表中。方案二：AT89C51AT89C51是一種帶4K字節(jié)FLASH存儲(chǔ)器的低電壓、高性能CMOS8位微處理器，俗稱(chēng)單片機(jī)。AT89C2051是一種帶2K字節(jié)閃存可編程可擦除只讀存儲(chǔ)器的單片機(jī)。單片機(jī)的可擦除只讀存儲(chǔ)器可以反復(fù)擦除1000次。該器件采用ATMEL高密度非易失存儲(chǔ)器制造技術(shù)制造，與工業(yè)標(biāo)準(zhǔn)的MCS-51指令集和輸出管腳相兼容。由于將多功能8位CPU和閃爍存儲(chǔ)器組合在單個(gè)芯片中，ATMEL的AT89C51是一種高效微控制器，AT89C2051是它的一種精簡(jiǎn)版本。AT89C51單片機(jī)為很多嵌入式控制系統(tǒng)提供了一種靈活性高且價(jià)廉的方案。設(shè)計(jì)需要2片MCU，都采用TI公司提供的MSP430G2xxx系列芯片。其中聲源產(chǎn)生模塊選用以MSP430G2452為核心的單片機(jī)最小系統(tǒng)；信息處理系統(tǒng)采用MSP430G2553為主的Launchpad作為數(shù)據(jù)處理和顯示模塊控制。2.1.4 顯示模塊方案一：LCD12864LCD12864為帶中文字庫(kù)的128X64 是一種具有4位/8位并行、2線(xiàn)或3線(xiàn)串行多種接口方式，內(nèi)部含有國(guó)標(biāo)一級(jí)、二級(jí)簡(jiǎn)體中文字庫(kù)的點(diǎn)陣圖形液晶顯示模塊。其顯示分辨率為12864, 內(nèi)置8192 個(gè)16*16 點(diǎn)漢字，和128 個(gè)16*8 點(diǎn)ASCII 字符集.利用該模塊靈活的接口方式和簡(jiǎn)單方便的操作指令，可構(gòu)成全中文人機(jī)交互圖形界面。可以顯示84 行1616 點(diǎn)陣的漢字. 也可完成圖形顯示.低電壓低功耗是其又一顯著特點(diǎn)。由該模塊構(gòu)成的液晶顯示方案與同類(lèi)型的圖形點(diǎn)陣液晶顯示模塊相比，不論硬件電路結(jié)構(gòu)或顯示程序都要簡(jiǎn)潔得多，且該模塊的價(jià)格也略低于相同點(diǎn)陣的圖形液晶模塊。方案二：LED顯示屏LED顯示屏：又稱(chēng)電子顯示屏或者飄字屏幕。是由LED點(diǎn)陣列和led pc 面板組成，通過(guò)紅色，藍(lán)色，綠色LED燈的亮滅來(lái)顯示文字、圖片、動(dòng)畫(huà)、視頻，內(nèi)容可以隨時(shí)更換，各部分組件都是模塊化結(jié)構(gòu)的顯示器件。傳統(tǒng)LED顯示屏通常由顯示模塊、控制系統(tǒng)及電源系統(tǒng)組成。顯示模塊由LED燈組成的點(diǎn)陣構(gòu)成，負(fù)責(zé)發(fā)光顯示；控制系統(tǒng)通過(guò)控制相應(yīng)區(qū)域的亮滅，可以讓屏幕顯示文字、圖片、視頻等內(nèi)容，單色、雙色屏主要用來(lái)播放文字的，全彩屏主要是播放動(dòng)畫(huà)的；電源系統(tǒng)負(fù)責(zé)將輸入電壓電流轉(zhuǎn)為顯示屏需要的電壓電流。本次大賽要求的是128*64以上分辨率的顯示屏，所以選擇LCD12864就能滿(mǎn)足設(shè)計(jì)要求。并且自帶字庫(kù)，簡(jiǎn)單方便。故本設(shè)計(jì)采用LCD顯示屏。2.1.5 定位算法選擇方案一：直角坐標(biāo)系法直接采用三個(gè)點(diǎn)定位的方法，利用函數(shù)關(guān)系式算出坐標(biāo)。如圖：圖5 直角坐標(biāo)系法測(cè)距根據(jù)距離不同，接收聲源就會(huì)產(chǎn)生時(shí)間差，兩個(gè)時(shí)間差，兩個(gè)變量，故可以求出（x，y）的坐標(biāo)值。x2+y-352-(x2+y2)=t1-t2*c(x-502+y2)- (x2+y2)=t2-t3*c其中c=340m/s。這種方法雖然思路簡(jiǎn)單，但是運(yùn)算量大，將會(huì)影響單片機(jī)運(yùn)算速度，增加我們的運(yùn)算難度，故不采用。方案二：歸一化正方形陣圖6 歸一化正方形歸一化正方形算法如圖，傳感器陣列采用正方形，傳感器的位置坐標(biāo)為（L，L），（-L，L），（-L，-L），（L，-L）。則聲源位置（x，y）可由下式算出（式中2L為正方陣的邊長(zhǎng)，t1，t2，t3分別為傳感器2，3，4相對(duì)于1的時(shí)差，c是傳播速度）：三硬件電路設(shè)計(jì) 3.1 系統(tǒng)框圖聲響模塊從單片機(jī)聲音接收LCD顯示主單片機(jī)語(yǔ)音播報(bào)控制圖7 系統(tǒng)總框圖系統(tǒng)主要由三大模塊組成：聲響模塊、聲音接收模塊、信號(hào)處理模塊。聲響模塊產(chǎn)生聲音信號(hào)，由聲音接收模塊接收信號(hào)并產(chǎn)生電流脈沖，經(jīng)總線(xiàn)系統(tǒng)傳送到信號(hào)處理模塊進(jìn)行運(yùn)算處理，將測(cè)試數(shù)據(jù)顯示在LCD顯示屏上。系統(tǒng)總電路圖見(jiàn)附錄二。3.2 聲響模塊圖8 聲響模塊電路圖通過(guò)單片機(jī)產(chǎn)生500Hz的方波信號(hào)，利用單管放大后給喇叭發(fā)聲。其中電位器可對(duì)音量進(jìn)行調(diào)節(jié)。3.3 從單片機(jī)最小系統(tǒng)圖9 從單片機(jī)最小系統(tǒng)單片機(jī)最小系統(tǒng)采用的是TI公司生產(chǎn)的超低功耗的MSP430G2452單片機(jī)為核心，其中9號(hào)端口為P2.1，實(shí)際電路中需和聲源模塊相連接。3.4聲音接收模塊圖10 接收系統(tǒng)模塊電路3.5信號(hào)處理模塊信號(hào)處理模塊由總線(xiàn)控制單元，MSP430G2553為核的Launchpad以及LCD顯示屏共同組成。單片機(jī)內(nèi)部運(yùn)算處理后將結(jié)果送入LCD顯示。圖11 主單片機(jī)及顯示3.6 語(yǔ)音模塊采用ISD4004語(yǔ)音錄放芯片制作成語(yǔ)音播報(bào)模塊。利用lm386語(yǔ)音功放芯片放大。四. 軟件設(shè)計(jì)4.1 軟件流程圖設(shè)計(jì)采用MSP430G2553為核心的Launchpad負(fù)責(zé)信號(hào)的處理并控制LCD顯示屏顯示相應(yīng)數(shù)據(jù)。主程序流程圖如下：開(kāi)始初始化MCU初始化LCD接收信號(hào)進(jìn)入中斷數(shù)據(jù)處理退出中斷LCD顯示數(shù)據(jù)結(jié)束中斷流程圖：進(jìn)入中斷判斷先后 x y z j顯示數(shù)據(jù)讀取坐標(biāo)退出中斷中斷程序開(kāi)始后，系統(tǒng)首先對(duì)聲音接收模塊采集到的信息進(jìn)行判斷，找到距離聲源最近的接收器，再按時(shí)間差分別得出其它3個(gè)接收器的距離差，再通過(guò)單片機(jī)就可以計(jì)算出聲源所在位置，發(fā)出屏幕顯示數(shù)據(jù)后退出中斷。額外加入了語(yǔ)音播報(bào)裝置，在每次采集測(cè)試數(shù)據(jù)開(kāi)始和結(jié)束都會(huì)進(jìn)行一次自動(dòng)語(yǔ)音播報(bào)。五 測(cè)試結(jié)果與分析5.1 測(cè)試方法與儀器 先測(cè)試4個(gè)定點(diǎn)（分別為（10，10）（45，10）（10，25）（45，25）來(lái)標(biāo)定4個(gè)聲音接收模塊的精度等級(jí)，然后采取隨機(jī)取點(diǎn)方式得到測(cè)試數(shù)據(jù)。測(cè)試中主要用到的儀器有直流穩(wěn)壓電源，示波器等。5.2 測(cè)試數(shù)據(jù)選中坐標(biāo)接收時(shí)間差測(cè)試坐標(biāo)誤差(cm) x y z j(35,15) 3611383471(39,15)4(25,10) 13108303237(23,12)3(40,20) 564135210(39,20)1(15,15) 13775295(21,17)5(25,15) 13108321237(23,12)3測(cè)試數(shù)據(jù)5.3 測(cè)試結(jié)果分析測(cè)試平均誤差在5cm以?xún)?nèi)，部分坐標(biāo)點(diǎn)能達(dá)到3cm標(biāo)準(zhǔn)，符合設(shè)計(jì)要求。 5.4 測(cè)試結(jié)果本設(shè)計(jì)制作完成了題目要求的基本部分的全部要求和發(fā)揮部分的大部分要求，達(dá)到設(shè)計(jì)要求。個(gè)別指標(biāo)由于時(shí)間有限只完成相應(yīng)的軟件和硬件設(shè)計(jì)，整體調(diào)試還未能全部完成。參考文獻(xiàn)1 范紅剛，魏學(xué)海，陳和.51單片機(jī)自學(xué)筆記；北京，北京航空航天大學(xué)出版社2010年1月第1版2 王宜懷，曹金華.嵌入式系統(tǒng)設(shè)計(jì)實(shí)戰(zhàn)；北京，北京航空航天大學(xué)出版社2011年5月第1版3 聞怡洋.無(wú)線(xiàn)設(shè)備編程指南；北京，北京大學(xué)出版社2004年7月第1版4 李玉柏.最小系統(tǒng)設(shè)計(jì)與應(yīng)用；四川，電子科技大學(xué)出版社2012年4月第1版5 鐘洪聲.電子電路設(shè)計(jì)技術(shù)基礎(chǔ)；四川，電子科技大學(xué)出版社2012年4月第1版6 王昊，李昕.集成運(yùn)放應(yīng)用電路設(shè)計(jì)360例；北京，電子工業(yè)出版社2007年1月7 喻金錢(qián)，喻斌.短距離無(wú)線(xiàn)通信詳解基于單片機(jī)控制；北京，北京航空航天大學(xué)出版社2009年4月附錄一：元器件清單元器件名數(shù)量MSP430G25531片MSP430G24521片LP2950-33LPRE31片LM2577S1片LM3934片MIC4個(gè)BUZZER1個(gè)穩(wěn)壓管78051個(gè)LCD128641個(gè)電位器若干電阻若干電容若干電池2節(jié)電感2個(gè)附錄二：系統(tǒng)總電路圖附錄三：程序#include "msp430g2553.h"#include "math.h"#define CS12864_SET P2OUT |=BIT0#define CS12864_CLR P2OUT &=BIT0#define SID12864_SET P2OUT |=BIT1#define SID12864_CLR P2OUT &=BIT1#define SCLK12864_SET P2OUT |=BIT2#define SCLK12864_CLR P2OUT &=BIT2signed int s_1=0;signed int s_2=0;unsigned char ss;unsigned char tank=0;unsigned char state=0;/4004unsigned int time=0;unsigned char i;unsigned int temp;#define ISD_SS_SET (P2OUT |=BIT4)#define ISD_SS_CLR (P2OUT &=BIT4)#define ISD_SCK_SET (P2OUT |=BIT3)#define ISD_SCK_CLR (P2OUT &=BIT3)#define ISD_MOSI_SET (P2OUT |=BIT5)#define ISD_MOSI_CLR (P2OUT &=BIT5)/*/ISD4002 spi串行發(fā)送子程序，8位數(shù)據(jù)/*void spi_send(unsigned char isdx) unsigned char isx_counter;ISD_SS_CLR; /ss=0,打開(kāi)spi通信端ISD_SCK_CLR;for(isx_counter=0;isx_counter<8;isx_counter+) /先發(fā)低位再發(fā)高位，依次發(fā)送。 if (isdx&0x01)=1)ISD_MOSI_SET;elseISD_MOSI_CLR;isdx=isdx>>1;ISD_SCK_SET;_delay_cycles(6);ISD_SCK_CLR;_delay_cycles(6);/*發(fā)送掉電指令，并延遲50msvoid isd_pd(void)/4004 _delay_cycles(10000);spi_send(0x20); ISD_SS_SET; _delay_cycles(60000);spi_send(0x20); ISD_SS_SET; _delay_cycles(120000);void isd_stop()/4004 _delay_cycles(1000); /*spi_send(0); /發(fā)送放音起始地址低位 _delay_cycles(3);spi_send(0); /發(fā)送放音起始地址高位 _delay_cycles(3);*/spi_send(0x10); /發(fā)送setplay指令字節(jié) ISD_SS_SET;void isd_setplay(unsigned char adl,unsigned char adh)/4004 _delay_cycles(10000);spi_send(0x20); ISD_SS_SET; _delay_cycles(25000);_delay_cycles(1000);spi_send(adl); /發(fā)送放音起始地址低位/_delay_cycles(3);spi_send(adh); /發(fā)送放音起始地址高位 / _delay_cycles(3);spi_send(0xE0); /發(fā)送setplay指令字節(jié)ISD_SS_SET; _delay_cycles(20);spi_send(0xF0); /發(fā)送setplay指令字節(jié) ISD_SS_SET;void isd_rec(unsigned char adl,unsigned char adh)/4004/4004 _delay_cycles(10000);spi_send(0x20); ISD_SS_SET; _delay_cycles(25000);isd_stop();spi_send(0x20); ISD_SS_SET; _delay_cycles(50000);_delay_cycles(1000);spi_send(adl); /發(fā)送放音起始地址低位spi_send(adh); /發(fā)送放音起始地址高位spi_send(0xa0); /發(fā)送setplay指令字節(jié)ISD_SS_SET; _delay_cycles(20);spi_send(0xb0); /發(fā)送setplay指令字節(jié) ISD_SS_SET;const unsigned char s15136=108,108,107,106,105,105,104,103,103,102,101,101,100,99,99,98,97,97,96,95,95,94,94,93,93,92,92,91,91,90,90,89,89,89,88,88,106,106,105,105,104,103,103,102,101,101,100,99,99,98,97,97,96,96,95,94,94,93,93,92,92,91,91,90,90,89,89,88,88,88,87,87,105,104,104,103,102,102,101,100,100,99,99,98,97,97,96,95,95,94,94,93,93,92,92,91,91,90,90,89,89,88,88,87,87,87,86,86,103,102,102,101,101,100,100,99,98,98,97,97,96,95,95,94,94,93,93,92,91,91,90,90,89,89,89,88,88,87,87,86,86,86,85,85,101,101,100,100,99,99,98,97,97,96,96,95,95,94,93,93,92,92,91,91,90,90,89,89,88,88,87,87,87,86,86,85,85,85,84,84,99,99,98,98,97,97,96,96,95,95,94,94,93,93,92,91,91,90,90,89,89,88,88,88,87,87,86,86,85,85,85,84,84,84,83,83,97,97,96,96,96,95,95,94,94,93,93,92,92,91,91,90,90,89,89,88,88,87,87,86,86,86,85,85,84,84,84,83,83,82,82,82,95,95,95,94,94,93,93,93,92,92,91,91,90,90,89,89,88,88,87,87,86,86,86,85,85,84,84,84,83,83,82,82,82,81,81,81,93,93,93,92,92,92,91,91,90,90,89,89,89,88,88,87,87,86,86,85,85,85,84,84,83,83,83,82,82,82,81,81,81,80,80,80,91,91,91,91,90,90,89,89,89,88,88,87,87,87,86,86,85,85,85,84,84,83,83,83,82,82,81,81,81,80,80,80,79,79,79,79,89,89,89,89,88,88,88,87,87,87,86,86,85,85,85,84,84,83,83,83,82,82,82,81,81,81,80,80,80,79,79,79,78,78,78,77,88,87,87,87,87,86,86,86,85,85,85,84,84,83,83,83,82,82,82,81,81,81,80,80,80,79,79,79,78,78,78,77,77,77,77,76,86,85,85,85,85,84,84,84,84,83,83,83,82,82,82,81,81,80,80,80,80,79,79,79,78,78,78,77,77,77,77,76,76,76,76,75,84,83,83,83,83,83,82,82,82,81,81,81,81,80,80,80,79,79,79,78,78,78,77,77,77,77,76,76,76,76,75,75,75,75,74,74,82,82,81,81,81,81,80,80,80,80,79,79,79,79,78,78,78,77,77,77,77,76,76,76,76,75,75,75,75,74,74,74,74,73,73,73,80,80,79,79,79,79,79,78,78,78,78,77,77,77,77,76,76,76,76,75,75,75,75,74,74,74,74,73,73,73,73,73,72,72,72,72,78,78,77,77,77,77,77,77,76,76,76,76,76,75,75,75,75,74,74,74,74,73,73,73,73,73,72,72,72,72,72,71,71,71,71,71,76,76,76,75,75,75,75,75,75,74,74,74,74,74,73,73,73,73,73,72,72,72,72,72,71,71,71,71,71,70,70,70,70,70,70,70,74,74,74,74,73,73,73,73,73,73,72,72,72,72,72,72,71,71,71,71,71,71,70,70,70,70,70,70,69,69,69,69,69,69,68,68,72,72,72,72,71,71,71,71,71,71,71,71,70,70,70,70,70,70,69,69,69,69,69,69,69,68,68,68,68,68,68,68,68,67,67,67,70,70,70,70,70,69,69,69,69,69,69,69,69,69,68,68,68,68,68,68,68,68,67,67,67,67,67,67,67,67,66,66,66,66,66,66,68,68,68,68,68,68,68,67,67,67,67,67,67,67,67,67,67,66,66,66,66,66,66,66,66,66,66,65,65,65,65,65,65,65,65,65,66,66,66,66,66,66,66,66,66,65,65,65,65,65,65,65,65,65,65,65,65,65,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,64,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,63,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,62,61,61,61,61,61,61,61,61,61,61,61,61,61,61,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,60,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,58,59,59,59,59,59,59,59,59,59,59,59,59,59,59,56,56,56,56,56,56,56,56,56,56,56,56,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,57,58,58,58,54,54,54,54,54,54,54,54,54,55,55,55,55,55,55,55,55,55,55,55,55,55,56,56,56,56,56,56,56,56,56,56,56,56,56,56,52,52,52,52,52,52,52,53,53,53,53,53,53,53,53,53,53,54,54,54,54,54,54,54,54,54,54,55,55,55,55,55,55,55,55,55,50,50,50,50,50,51,51,51,51,51,51,51,51,51,52,52,52,52,52,52,52,52,53,53,53,53,53,53,53,53,54,54,54,54,54,54,48,48,48,48,49,49,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,51,52,52,52,52,52,52,52,52,53,53,53,46,46,46,46,47,47,47,47,47,47,48,48,48,48,48,48,49,49,49,49,49,49,50,50,50,50,50,50,51,51,51,51,51,51,52,52,44,44,44,45,45,45,45,45,45,46,46,46,46,46,47,47,47,47,47,48,48,48,48,48,49,49,49,49,49,50,50,50,50,50,50,50,42,42,43,43,43,43,43,43,44,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47,47,48,48,48,48,48,49,49,49,49,49,40,40,41,41,41,41,41,42,42,42,42,43,43,43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,47,47,48,48,48,48,38,38,39,39,39,39,40,40,40,40,41,41,41,41,42,42,42,43,43,43,43,44,44,44,44,45,45,45,45,46,46,46,46,47,47,47,36,37,37,37,37,37,38,38,38,39,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43,43,44,44,44,44,45,45,45,45,46,46,34,35,35,35,35,36,36,36,36,37,37,37,38,38,38,39,39,40,40,40,40,41,41,41,42,42,42,43,43,43,43,44,44,44,44,45,32,33,33,33,33,34,34,34,35,35,35,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,43,43,43,44,31,31,31,31,32,32,32,33,33,33,34,34,35,35,35,36,36,37,37,37,38,38,38,39,39,39,40,40,40,41,41,41,42,42,42,43,29,29,29,29,30,30,31,31,31,32,32,33,33,33,34,34,35,35,35,36,36,37,37,37,38,38,39,39,39,40,40,40,41,41,41,41,27,27,27,28,28,28,29,29,30,30,31,31,31,32,32,33,33,34,34,35,35,35,36,36,37,37,37,38,38,38,39,39,39,40,40,40,25,25,25,26,26,27,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,34,35,35,36,36,36,37,37,38,38,38,39,39,39,23,23,24,24,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,34,34,34,35,35,36,36,36,37,37,38,38,38,21,21,22,22,23,23,24,24,25,25,26,26,27,27,28,29,29,30,30,31,31,32,32,32,33,33,34,34,35,35,35,36,36,36,37,37,19,19,20,20,21,21,22,23,23,24,24,25,25,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,33,34,34,35,35,35,36,36,17,18,18,19,19,20,20,21,22,22,23,23,24,25,25,26,26,27,27,28,29,29,30,30,31,31,31,32,32,33,33,34,34,34,35,35,15,16,16,17,18,18,19,20,20,21,21,22,23,23,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,33,33,33,34,34,14,14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,24,25,26,26,27,27,28,28,29,29,30,30,31,31,32,32,32,33,33,12,12,13,14,15,15,16,17,17,18,19,19,20,21,21,22,23,23,24,25,25,26,26,27,27,28,28,29,29,30,30,31,31,31,32,32,;const unsigned char s25136=93,92,90,88,86,84,82,80,78,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,42,40,38,36,34,32,30,28,27,93,91,89,87,86,84,82,80,78,76,74,73,71,69,67,65,63,61,59,57,55,53,51,49,47,46,44,42,40,38,36,34,33,31,29,27,92,90,89,87,85,83,82,80,78,76,74,72,70,69,67,65,63,61,59,57,55,53,51,50,48,46,44,42,40,38,37,35,33,31,30,28,91,90,88,87,85,83,81,80,78,76,74,72,70,68,67,65,63,61,59,57,55,53,52,50,48,46,44,42,40,39,37,35,33,32,30,29,91,89,88,86,84,83,81,79,77,76,74,72,70,68,66,65,63,61,59,57,55,54,52,50,48,46,44,43,41,39,37,36,34,32,31,29,90,89,87,86,84,82,81,79,77,75,74,72,70,68,66,65,63,61,59,57,55,54,52,50,48,46,45,43,41,39,38,36,34,33,31,30,89,88,87,85,83,82,80,79,77,75,73,72,70,68,66,64,63,61,59,57,56,54,52,50,48,47,45,43,41,40,38,37,35,33,32,31,89,87,86,84,83,81,80,78,76,75,73,71,70,68,66,64,63,61,59,57,56,54,52,50,49,47,45,44,42,40,39,37,36,34,33,31,88,87,85,84,82,81,79,78,76,75,73,71,69,68,66,64,63,61,59,57,56,54,52,51,49,47,45,44,42,41,39,38,36,35,33,32,88,86,85,83,82,80,79,77,76,74,73,71,69,68,66,64,63,61,59,57,56,54,52,51,49,47,46,44,43,41,40,38,37,35,34,32,87,86,84,83,82,80,79,77,75,74,72,71,69,67,66,64,62,61,59,58,56,54,53,51,49,48,46,45,43,41,40,38,37,36,34,33,86,85,84,82,81,80,78,77,75,74,72,70,69,67,66,64,62,61,59,58,56,54,53,51,50,48,46,45,43,42,40,39,38,36,35,34,86,85,83,82,81,79,78,76,75,73,72,70,69,67,66,64,62,61,59,58,56,54,53,51,50,48,47,45,44,42,41,39,38,37,35,34,85,84,83,81,80,79,77,76,75,73,72,70,69,67,65,64,62,61,59,58,56,55,53,51,50,48,47,45,44,43,41,40,39,37,36,35,85,83,82,81,80,78,77,76,74,73,71,70,68,67,65,64,62,61,59,58,56,55,53,52,50,49,47,46,44,43,42,40,39,38,37,35,84,83,82,81,79,78,77,75,74,72,71,70,68,67,65,64,62,61,59,58,56,55,53,52,50,49,48,46,45,43,42,41,39,38,37,36,84,82,81,80,79,78,76,75,74,72,71,69,68,67,65,64,62,61,59,58,56,55,53,52,51,49,48,46,45,44,42,41,40,39,38,36,83,82,81,80,78,77,76,75,73,72,71,69,68,66,65,64,62,61,59,58,56,55,54,52,51,49,48,47,45,44,43,42,40,39,38,37,83,82,80,79,78,77,76,74,73,72,70,69,68,66,65,63,62,61,59,58,57,55,54,52,51,50,48,47,46,44,43,42,41,40,38,37,82,81,80,79,78,76,75,74,73,71,70,69,67,66,65,63,62,61,59,58,57,55,54,53,51,50,49,47,46,45,44,42,41,40,39,38,82,81,80,78,77,76,75,74,72,71,70,69,67,66,65,63,62,61,59,58,57,55,54,53,51,50,49,48,46,45,44,43,42,40,39,38,81,80,79,78,77,76,75,73,72,71,70,68,67,66,65,63,62,61,59,58,57,55,54,53,52,50,49,48,47,45,44,43,42,41,40,39,81,80,79,78,77,75,74,73,72,71,69,68,67,66,64,63,62,61,59,58,57,56,54,53,52,51,49,48,47,46,45,43,42,41,40,39,80,79,78,77,76,75,74,73,72,70,69,68,67,66,64,63,62,61,59,58,57,56,54,53,52,51,50,48,47,46,45,44,43,42,41,40,80,79,78,77,76,75,74,73,71,70,69,68,67,65,64,63,62,61,59,58,57,56,55,53,52,51,50,49,47,46,45,44,43,42,41,40,80,79,78,77,76,74,73,72,71,70,69,68,67,65,64,63,62,61,59,58,57,56,55,53,52,51,50,49,48,47,46,44,43,42,41,40,79,78,77,76,75,74,73,72,71,70,69,68,66,65,64,63,62,61,59,58,57,56,55,54,52,51,50,49,48,47,46,45,44,43,42,41,79,78,77,76,75,74,73,72,71,70,69,67,66,65,64,63,62,61,59,58,57,56,55,54,53,51,50,49,48,47,46,45,44,43,42,41,78,78,77,76,75,74,73,72,70,69,68,67,66,65,64,63,62,61,59,58,57,56,55,54,53,52,51,50,48,47,46,45,44,43,42,42,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,77,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,43,77,76,75,74,74,73,72,71,70,69,68,67,66,65,64,63,62,61,59,58,57,56,55,54,53,52,51,50,49,48,47,46,46,45,44,43,77,76,75,74,73,72,71,70,70,69,68,67,66,65,64,63,62,61,59,58,57,56,55,54,53,52,51,50,50,49,48,47,46,45,44,43,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,76,75,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,45,44,76,75,74,73,73,72,71,70,69,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,51,50,49,48,47,47,46,45,44,76,75,74,73,72,71,71,70,69,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,51,50,49,49,48,47,46,45,44,75,75,74,73,72,71,70,70,69,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,51,50,50,49,48,47,46,45,45,75,74,74,73,72,71,70,69,69,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,51,51,50,49,48,47,46,46,45,75,74,73,73,72,71,70,69,68,68,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,52,52,51,50,49,48,47,47,46,45,75,74,73,72,72,71,70,69,68,67,67,66,65,64,63,62,61,60,60,59,58,57,56,55,54,53,53,52,51,50,49,48,48,47,46,45,74,74,73,72,71,7