OpenCV ピクセル操作デモ
2021.5.20 Coskx Lab
1 はじめに
OpenCVのMatからpixelデータを抜き出して操作します。
OpenCVのグレイスケール画像データはMat(のインスタンス)の中の2次元データであることは確かだけれど,直接操作することは出来ません。
Mat(のインスタンス)に対してメソッドgetの操作すると画像2次元配列を1次元配列に変換して取り出すことができます。
取り出せたら,ピクセル毎に自由に操作ができます。
ここでは,簡単な操作の例として,グレースケール画像データの最上行の左端から右側に走査し,
2番目の行を同様に左端から右側に走査し,3番目の行を同様に左端から右側に走査し,・・・
を繰り返し,最初に見つかる黒いデータを捜して,画像中のその位置に印を付けるデモを載せます。
この作業はスクリーンに見えている画像全体に対して行うことを想定していますが,スクリーンに見えている画像の部分矩形に対しても行ってみます。
2 デモアプリについて
デモアプリ
デモアプリでは,カメラ画像を表示している画面をタップするたびに,次の7この表示が順に現れます。
(1)最初は,カメラから得られたカラー画像を表示し,(2)次にグレースケール画像(モノクロ画像)を表示します。
(3)続いて,グレースケール画像に対してキャニーフィルタリングした画像を表示します。
(4)そして,表示画像内に位置大きさを指定して矩形を重ね描きして表示します。(5)次に表示画像内に位置と半径を指定して円を描きます。
ここまでが準備の意味の表示で,さらにタップすると本題の次の処理結果を表示します。
(6)表示画像用としてカラー画像を取得します。同時に解析用としてグレースケール画像も取得します。
グレースケール画像全体について,ピクセルデータをbyte型変数の1次元配列で取り出します。
1次元配列として,先頭から順に輝度をチェックして,黒画素(輝度が小さい画素)を捜します。
最初に見つかった配列要素番号をもとに,2次元座標の位置を求めます。元の画像データの幅がわかっていれば,
(見つかった配列要素番号)÷(元の画像データの幅)の整数演算で縦(行番号)がわかり,この割り算の余りが横(列番号)になります。
求まったら,カラー画像で,その位置に円を重ね描きます。
(7)さらに画面をタップすると次の処理結果を表示します。
グレースケール画像の一部分を矩形に切り取ったグレースケール画像を作ります。
この時使うのがsubmat()というメソッドです。
切り取ったグレースケール画像に対して,黒いピクセルを捜し,見つかった点に円を描きます。
検出領域を示す矩形を表示用カラー画像に重ね描きしています。
プログラムにおける作業場所
OpenCVのAndroid版ではMainActivityのメソッドonCameraFrame()が画像処理の部分です。,
カメラからの画像はカメラの準備ができ次第,このメソッド(関数)に繰り返し送られてきます。
メソッドが終わるときに戻り値Mat(のインスタンス,ここではmMat)を返すと,mMatが画面に表示されます。
このメソッドに送られてくるのはinputFrameで,inputFrame.rgba()またはinputFrame.gray()でMatに変換します。
メソッドget()について
Mat型のインスタンスmyMatとするとmyMatからピクセルデータを一次元データとして抜き出すためには,あらかじめmyMatのピクセル数と同じサイズのbyte型配列を用意する必要があります。
例えばbuffという名前でbyte型配列が準備できたら,
myMat.get(0, 0, buff);
で抜き出すことができます。(myMatには何も影響ありません)
抜き出されたデータは,画像の最上部行のデータ行,2番目のデータ行,3番目のデータ行,・・・が全て1列につながって,1次元データとなっています。
mMat中の画素数は(myMat.total() * myMat.channels())になります。(グレースケール画像では,myMat.channels()は1です。)
(https://coskxlabsite.stars.ne.jp/html/android/OpenCV_Mat.html 参照)
メソッドget()で得られた画素データの配列について
グレースケールpixelデータは符号無しなので0が最低輝度(黒),255が最大輝度(白)で値の範囲が0から255です。
しかし,byte型は符号有りと解釈されるので,値の範囲が-128から127です。このままではピクセルの輝度の比較ができません。
そこで,最上位bitの0・1を反転します。そうするとbyte型変数で-128が黒,127が白として輝度を比較することができるようになります。
この手法は2の補数表現変換の常套手段です。
[デモアプリの表示(6)(7)]では,-64より小さな値なら黒と判断していました。
3 使用環境
- Windows 10 64-bit
- Android Studio 4.1.3
- OpenCV 4.5.2
4 準備
まず,新規プロジェクトをEmpty Projectとして作ることにします。
パッケージ名が設定されるのでこの後はそのパッケージ名を使います。
パッケージ名は生成されたMainActivity.javaの先頭行に書いてあります。
「
OpenCV4.5.5のカメラプレビュー」記事の手順で次の作業を行います。
(1)OpenCVモジュールを取り込みます。
(2)AndroidManifast.xmlを修正します。
その続きからの作業になります。
5 追加作業
MainActivity.javaとlayout/activity_main.xmlを修正します。
作業中のパッケージ名を壊さないように気を付けてください。
files.zipのダウンロード
6 MainActivity.java
このデモアプリでは,activity_main.xmlのViewのところに
android:layout_height="match_parent"
android:clickable="true"
が仕掛けてあって,起動後に画面をタップすることで
MainActivity.javaのメソッド
public void clicedwork(View v)
が呼ばれて,変数modeが切り替わっていき,表示が変化します。
MainActivity.javaのメソッド
public Mat onCameraFrame(CvCameraViewFrame inputFrame)
でmodeの値によって表示方法が切り替えられています。
黒のピクセルを見つけているのはmodeが5の時で,矩形内で黒のピクセルを見つけているのはmodeが6の時です。
MainActivity.java抜粋
//カメラからの画像はカメラの準備ができ次第,このメソッド(関数)に繰り返し送られる。
//戻り値Matを返すと,Matが画面に表示される。
//このメソッドに送られてくるのはinputFrameで,inputFrame.rgba()またはinputFrame.gray()でMatに変換される
public Mat onCameraFrame(CvCameraViewFrame inputFrame) {
if (mode == 0) {
mMat = inputFrame.rgba(); //RGBA形式Matへの変換
} else if (mode == 1) {
mMat= inputFrame.gray(); //グレースケール形式Matへの変換
} else if (mode == 2) {
Imgproc.Canny(inputFrame.gray(), mMat, 100, 200); //grayscale canny
filtering
//inputFrame.gray()でグレースケール画像を受け取り,キャニーフィルタした値がmMatに入る
} else if (mode == 3) {
//青の矩形を描く
//画像では左上が座標(0,0)で横軸は右方向,縦軸は下方向が正の方向となる
mMat = inputFrame.rgba();
int left = mMat.width()*4/10;//画像幅の4/10をleftにする
int right = mMat.width()*6/10;//画像幅の6/10をrightにする
int top = mMat.height()*4/10;//画像高さの4/10をtopにする
int bottom = mMat.height()*6/10;//画像高さの6/10をbottomにする
Point lt0 = new Point(left, top);//矩形左上の点の座標
Point rb0 = new Point(right, bottom);//矩形右下の点の座標
Imgproc.rectangle(mMat, lt0, rb0, new Scalar(2, 157, 240), 2);
//mMatにlt0とrb0を頂点とする矩形を描いている
//Scalar(r,g,b)は色を指定している
//2は線の太さを指定している
} else if (mode == 4) {
//円を描く
mMat = inputFrame.rgba();
Point
center = new Point(mMat.width()*4/10, mMat.height()*4/10);//中心座標緯
int radius = mMat.width()*5/100;//半径
Imgproc.circle(mMat,center, radius, new Scalar(250, 0, 0), 2);
//mMatにcenterを中心とする半径radiusの円を描いている
//Scalar(r,g,b)は色を指定している
//2は線の太さを指定している
} else if (mode == 5) {
//画面左上の黒い矩形頂点を見つけて円を描く
//ただし画面では黒い矩形の上部と左側は白いものとする
//画像をバイト列に変換して,走査すると,最初の黒ピクセルを見つけることができる
//mMatは表示用,mMatAnalysisは作業用
mMat = inputFrame.rgba(); //RGBA形式Matへの変換
Mat mMatAnalysis= inputFrame.gray(); //検出用グレースケール形式Matへの変換
byte[] bytebuff= new byte[(int) (mMatAnalysis.total() *
mMatAnalysis.channels())];
mMatAnalysis.get(0, 0, bytebuff); //mat内のすべてのデータの取得
//https://coskxlabsite.stars.ne.jp/html/android/OpenCV_Mat.html 参照
//画像は2次元データだが,一次元配列として受け取る
//画像の最上部行のデータ行,2番目のデータ行,3番目のデータ行,・・・が全て1列につながって,1次元データとなっている
int i;
for
(i=0; i<bytebuff.length; i++) bytebuff[i] ^= 0x80; //黒:-128 白:127 に変換
for (i=0; i<bytebuff.length; i++) {
if (bytebuff[i]<-64) break; //暗いピクセル発見
}
int width = mMatAnalysis.width();
int y = i / width;
int x = i % width;
Point center = new Point(x, y);//中心座標緯
int radius = width*5/100;//半径
Imgproc.circle(mMat,center, radius, new Scalar(250, 0, 0), 2);
} else if (mode == 6) {
//指示した矩形の範囲で黒い矩形頂点を見つけて円を描く
//ただし指示した矩形の範囲では黒い矩形の上部と左側は白いものとする
//画像をバイト列に変換して,走査すると,最初の黒ピクセルを見つけることができる
//mMatは表示用,それ以外のMatインスタンス(変数)は作業用
mMat = inputFrame.rgba(); //RGBA形式Matへの変換
Mat mMatAnalysis= inputFrame.gray(); //検出用グレースケール形式Matへの変換
int left = mMatAnalysis.width()*4/10;//画像幅の4/10をleftにする
int right = mMatAnalysis.width()*6/10;//画像幅の6/10をrightにする
int top = mMatAnalysis.height()*4/10;//画像高さの4/10をtopにする
int bottom = mMatAnalysis.height()*6/10;//画像高さの6/10をbottomにする
Point lt0 = new Point(left, top);//矩形左上の点の座標
Point rb0 = new Point(right, bottom);//矩形右下の点の座標
Imgproc.rectangle(mMat, lt0, rb0, new Scalar(2, 157, 240), 2);
Rect mRect = new Rect(lt0,rb0);//矩形を定義(青い矩形と同じ位置と大きさ)
Mat
mMatMyArea = mMatAnalysis.submat(mRect); //mMatAnalysisから矩形に切り出す
byte[] bytebuff= new byte[(int) (mMatMyArea.total() *
mMatMyArea.channels())];
mMatMyArea.get(0, 0, bytebuff); //mat内のすべてのデータの取得
int i;
for
(i=0; i<bytebuff.length; i++) bytebuff[i] ^= 0x80; //黒:-128 白:127 に変換
for (i=0; i<bytebuff.length; i++) {
if (bytebuff[i]<-64) break; //暗いピクセル発見
}
if (i == bytebuff.length) i = bytebuff.length-1; //見つからなかった
int width = mMatMyArea.width();
int y = i / width + top;
int x = i % width + left;
Point center = new Point(x, y);//中心座標緯
int radius = mMatAnalysis.width() * 3/100;//半径
Imgproc.circle(mMat,center, radius, new Scalar(250, 0, 0), 2);
}
return mMat;//ここでmMatを返すことによって画像がスクリーンに表示される
}
//スクリーンに表示されている画像をタップ(クリック)するとこのメソッドが呼ばれる
//この仕組みはLayout/activitu_main.xmlに記述されている「android:onClick="clicedwork"」で出来ている
public void clicedwork(View v) {
mode++;
//Toast.makeText(getApplicationContext(), "Test OK! mode = " + mode,
Toast.LENGTH_SHORT).show();
if (mode == 7) mode = 0;
}
7 実行の様子
実行時のスクリーンショットです。1つ目はmode5で2つ目はmode6です。
画像はPCのディスプレイ上の塗りつぶした黒の矩形が2つ描かれたデモ画像です。
静止画ではわかりませんが,デバイスを動かして画面を揺らしても,赤い丸が追従してきます。
全画面から黒いピクセル(左上から検索して最初に見つかった)を捜した結果
画面全体が検索対象なので,右下の矩形は検出されません。
青い矩形領域から黒いピクセル(左上から検索して最初に見つかった)を捜した結果
青い矩形領域が検索対象なので,左上の矩形は検出されません。
8 終わりに
・OpenCVでピクセルを抜き出して簡単な操作を行うデモを紹介しました。
参考1 1byteデータにおける符号なし解釈と符号有り解釈
1byteデータは8bitの値です。同じ値でも「符号有りの解釈」と「符号なしの解釈」では大小関係が異なります。
画素の輝度値は「符号なしの解釈」で,値が大きいほど明るい画素となります。
0111 1111(127)より1000 0000(128)の方が明るいことになります。
しかしjavaのbyte型変数では「符号有りの解釈」となっているので,同じ比較が
0111 1111(127)と1000 0000(-128)となってしまい明るさ比較が逆転してしまいます。
この問題を解決するには,画素の明るさを表すbyte型変数の最上位bitを反転させます。
そうすると,一番暗い値が-128で一番明るい値が127となって,値で明るさを比較できるようになります。
1byteデータの解釈の違いの表
bit表現 | 符号なし解釈 | 符号あり解釈 |
1111 1111 | 255 | -1 |
1111 1110 | 254 | -2 |
1111 1101 | 253 | -3 |
: | : | : |
1000 0010 | 130 | -126 |
1000 0001 | 129 | -127 |
1000 0000 | 128 | -128 |
0111 1111 | 127 | 127 |
0111 1110 | 126 | 126 |
: | : | : |
0000 0010 | 2 | 2 |
0000 0001 | 1 | 1 |
0000 0000 | 0 | 0 |
参考2 デモアプリmode6の時の青い矩形内の画像データ抜き出し例
デモアプリmode6の時の青い矩形内の画像データ抜き出し例を示します。
青い矩形領域内の右下側に黒い矩形が見えている様子です。
画像データは2次元配列ですが,抜き出したbyte配列は1次元です。
ここでは,見やすいように,1次元データを矩形幅ごとに改行して表示しています。
値表示の右下に負の値(輝度の低い)の領域が見えると思います。(表示をスクロールすると見えます。)
0: 90 90 89 89 89 88 89 89 89 89 88 88 89 90 90 92 93 93 92 91 90 89 90 90 92 93 92 93 94 94 95 94 92 91 91 89 87 88 89 90 90 90 92 94 95 96 96 96 94 93 92 91 91 92 91 93 95 95 95 96 97 97 96 94 92 90 90 90 90 90 92 92 92 93 94 95 92 92 91 89 89 90 92 92 91 90 90 89 88 87 86 86 85 85 86 87 88 89 89 89 90 91 87 83 81 81 82 83 86 90 91 92 92 90 90 90 90 89 89 90 92 94 93 95 95 94 93 92 92 91 90 92 94 95 94 92 90 89 88 85 86 89 90 91 91 92 93 93 94 93 92 91 92 92 96 98 98 97 96 93 91 91 91 90 89 88 92 93 94 94 92 92 91 89 89 91 90 88 88 88 87 86 84 83 84 82 83 86 86 86 86 85 85 86 87 89 91 89 86 85 84 84 83 83 83 83 83 84 86 86 87 86 83 80 79 79 81 83 85 85 86 86 85 85 85 85 87 88 89 90 92 92 92 93 92 91 91 89 88 88 90 90 89 87 86 85 84 84 86 88 90 93 93 91 89 88
1: 90 89 88 87 87 88 88 89 88 88 88 88 88 89 89 90 92 93 93 92 92 91 88 89 89 90 90 91 93 94 95 94 95 96 96 92 89 90 90 92 91 90 92 94 96 96 96 96 94 93 92 92 92 92 93 94 94 94 94 94 92 93 92 92 91 90 90 91 91 92 92 92 93 94 94 93 89 89 86 83 87 89 91 91 90 90 88 88 88 86 86 86 85 85 85 86 86 89 88 89 89 90 89 88 87 86 86 88 91 91 90 90 90 90 89 88 87 87 88 90 92 94 96 97 96 96 96 96 94 94 93 94 95 96 94 93 92 90 87 86 87 91 92 92 92 93 93 94 94 92 91 90 91 93 94 95 94 93 93 90 87 87 89 90 90 91 92 93 95 95 94 92 91 90 90 89 88 87 88 88 87 86 85 85 83 81 82 84 86 86 86 87 87 88 88 88 89 88 87 85 84 83 83 83 82 83 82 83 84 85 86 85 84 84 84 83 84 86 88 89 88 88 87 85 84 84 86 89 89 89 90 90 89 90 91 91 91 91 91 92 92 94 93 91 88 86 86 87 88 89 92 93 93 91 91 90
2: 89 87 86 86 86 86 86 86 86 86 85 85 85 85 85 86 87 88 89 89 89 88 86 86 84 86 91 92 92 93 93 93 93 93 93 94 94 93 92 93 93 94 96 96 98 98 99 98 96 95 94 93 94 94 94 95 95 96 97 97 96 96 94 93 90 90 90 90 91 92 92 94 95 95 95 95 93 90 89 87 84 85 87 89 88 89 89 88 87 85 83 83 83 83 83 84 84 85 85 85 85 84 82 83 86 86 85 86 88 90 90 89 90 89 87 84 84 85 87 91 92 93 93 94 94 94 94 93 94 95 96 97 98 98 97 94 93 91 89 89 90 93 95 96 95 95 94 95 96 94 93 93 94 95 95 95 95 94 93 90 89 89 91 91 89 91 92 93 95 95 94 92 91 91 91 92 91 90 90 89 88 85 81 82 83 80 82 83 84 85 85 85 85 85 86 85 85 85 84 83 81 81 80 80 81 81 80 80 80 80 81 81 81 81 82 83 84 85 85 84 85 84 81 83 84 83 82 85 87 88 89 89 88 88 90 89 89 89 89 90 90 90 90 89 88 88 88 91 92 93 96 96 95 93 92 93
3: 90 90 88 87 86 87 86 84 85 85 85 86 85 86 86 85 86 87 87 89 90 89 87 85 83 88 91 90 90 90 91 91 92 92 91 91 91 91 91 91 90 91 95 97 97 96 97 98 97 94 93 94 94 96 96 96 96 97 97 97 97 96 94 92 92 92 93 94 94 92 93 96 96 96 96 95 95 94 93 93 93 91 90 90 89 91 91 89 88 85 84 85 85 85 84 85 85 85 85 85 85 83 81 82 86 88 87 86 87 88 88 86 86 85 85 81 80 81 82 86 90 92 92 93 94 93 92 90 89 89 91 94 96 95 92 90 91 90 89 91 92 95 94 94 95 95 95 96 95 93 93 95 95 96 96 95 94 93 92 90 90 89 89 91 93 94 94 95 96 96 95 92 93 95 94 94 95 93 93 91 89 88 88 88 91 90 91 93 93 93 88 85 84 84 83 83 85 84 84 83 81 81 81 81 82 82 81 80 80 81 81 82 82 84 83 83 83 82 81 81 79 78 78 79 79 80 81 81 82 83 81 79 79 80 82 82 83 83 85 88 87 86 87 87 86 86 88 88 88 89 90 92 91 90 90 91
4: 93 94 93 91 90 90 89 77 78 86 87 87 86 87 88 88 87 88 88 88 89 91 91 89 86 87 89 91 90 90 91 91 91 90 90 90 90 90 90 90 90 91 93 92 93 95 96 97 96 94 92 93 94 93 94 94 94 94 95 95 95 93 92 90 89 90 90 91 92 92 95 97 96 97 97 96 96 93 92 93 93 92 92 92 93 95 94 94 94 90 88 87 87 87 86 84 87 89 89 89 88 87 87 88 89 90 90 88 89 90 88 87 86 85 86 87 86 86 86 87 87 88 89 89 91 90 90 89 89 89 90 93 94 95 93 91 89 87 88 87 87 89 91 92 92 93 94 92 90 90 91 93 94 94 94 93 92 89 88 88 89 89 88 90 91 90 90 91 91 91 91 92 95 96 95 95 95 95 94 92 90 89 87 87 89 91 93 93 93 92 91 91 91 91 90 89 89 88 88 86 85 84 83 79 80 82 83 83 83 84 85 86 87 88 88 86 86 85 85 83 81 81 81 81 80 81 83 84 85 84 84 84 83 85 87 88 87 85 84 83 81 80 80 81 81 82 85 89 90 90 91 92 91 91 91 91
5: 92 91 91 92 92 91 88 75 76 88 88 87 84 84 89 89 89 89 89 89 89 90 91 91 89 88 88 89 91 93 93 94 93 91 90 88 89 89 89 89 91 92 94 94 95 97 96 97 96 95 94 93 93 93 93 92 92 92 93 95 94 92 90 89 88 88 89 88 90 92 93 92 93 94 95 94 93 94 93 92 94 93 94 94 93 94 94 93 91 87 86 89 88 87 86 85 87 89 89 89 89 88 89 90 92 92 92 90 90 91 89 88 87 86 87 87 86 86 86 87 89 90 89 89 88 88 88 87 87 88 89 90 92 94 94 92 90 89 89 90 91 91 94 96 94 94 93 91 91 92 91 92 93 93 93 93 92 90 88 88 88 89 90 92 92 91 89 90 90 88 89 91 91 93 94 94 93 90 88 86 88 90 88 88 92 94 95 94 93 92 91 89 89 90 92 91 90 87 88 89 88 86 82 77 79 85 86 86 86 87 87 86 87 88 88 87 87 85 84 83 82 82 81 82 81 82 84 84 85 86 86 85 85 87 87 88 87 87 86 85 84 82 80 83 86 84 82 86 89 90 91 90 90 88 88 88
6: 94 92 89 87 87 85 83 82 84 88 90 88 87 87 87 88 88 86 86 86 87 88 88 88 88 88 88 87 87 88 90 92 91 90 89 90 90 88 88 89 89 90 91 92 95 96 97 99 99 98 97 96 95 94 94 94 95 95 96 96 95 93 91 90 89 88 89 90 92 95 96 95 96 97 96 96 95 94 93 92 93 93 93 93 93 94 95 94 92 90 87 88 88 86 83 84 86 88 89 88 88 86 85 84 83 83 84 87 87 86 86 86 85 85 84 85 84 84 84 85 85 86 85 86 85 85 85 87 88 89 91 92 92 93 92 90 88 87 87 87 89 90 92 95 96 96 96 96 98 99 96 93 94 96 96 94 93 92 91 91 90 91 93 94 94 94 92 92 92 91 91 92 92 93 95 95 94 92 91 89 88 88 87 87 90 92 93 93 94 93 90 90 90 91 91 91 91 90 88 87 85 82 78 77 79 82 84 85 86 85 80 81 83 84 85 85 85 82 81 80 80 80 80 80 79 80 82 83 83 83 82 83 83 84 84 85 85 84 85 83 81 80 81 81 85 85 83 83 83 85 86 86 86 86 85 85
7: 93 93 92 92 91 89 88 86 88 89 88 88 89 88 88 87 85 84 84 84 85 86 87 86 86 86 86 86 87 87 88 87 86 87 87 88 86 83 84 86 87 89 91 92 93 94 94 94 94 94 93 95 96 96 95 96 96 97 98 97 95 95 93 92 91 91 91 91 93 96 98 98 97 98 98 98 96 95 94 96 97 97 97 95 97 98 96 93 92 92 91 90 89 90 92 93 94 94 92 87 86 84 84 85 83 84 85 87 87 86 86 85 84 84 84 82 82 81 81 82 83 84 85 85 85 84 84 84 85 86 87 88 88 86 85 85 86 86 86 86 88 90 92 93 94 94 92 92 92 92 91 93 97 97 96 95 94 92 91 91 91 92 94 94 94 94 93 94 94 93 94 94 94 96 97 95 95 94 92 91 89 90 92 93 94 95 96 96 97 97 95 92 91 91 91 93 93 92 90 89 88 88 87 87 90 91 90 89 88 85 83 81 79 82 85 85 84 81 80 81 82 80 79 80 79 80 80 81 80 80 80 82 83 83 83 83 82 81 80 79 77 76 78 78 80 81 83 82 80 80 79 80 80 79 80 80
8: 94 94 94 93 92 90 90 90 90 90 90 90 90 89 88 86 86 87 87 87 88 88 88 88 88 88 87 88 89 89 88 87 88 88 89 88 87 88 86 85 84 84 85 87 91 92 92 93 94 94 92 91 92 92 92 92 92 94 97 95 93 92 92 92 91 90 91 91 93 95 96 96 95 95 96 94 93 93 94 94 94 94 96 95 98 99 98 94 92 92 92 90 90 91 91 92 93 94 95 95 94 91 90 88 89 90 90 89 90 91 89 86 84 84 85 83 83 83 84 85 86 86 85 85 86 86 86 87 87 87 88 87 87 86 85 84 83 84 81 82 86 90 91 91 92 93 91 88 88 89 89 91 92 95 94 91 89 88 88 89 89 90 92 94 94 94 94 94 93 92 92 93 93 95 94 92 90 89 89 89 89 89 90 92 93 94 94 94 96 95 94 94 95 95 96 95 93 91 90 91 91 89 89 88 89 91 92 93 92 90 89 89 87 88 92 89 86 85 85 84 83 81 82 82 83 83 82 82 82 83 84 86 86 85 85 85 84 82 81 80 78 78 78 78 79 80 81 81 82 82 82 82 83 83 84 84
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