delete pics to save space

lib.py

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+from sys import *
+
+# IO
+def isprint(ch):
+    isp=['A','B','C','D','E','F','G','H','I','J','K','L','M','N','O','P','Q','R','S','T','U','V','W','X','Y','Z',
+         'a','b','c','d','e','f','g','h','i','j','k','l','m','n','o','p','q','r','s','t','u','v','w','x','y','z',
+         '0','1','2','3','4','5','6','7','8','9',
+         '~','`','!','@','#','$','%','^','&','*','(',')',
+         '-','_','=','+','[','{',']','}','\\','|',
+         ';',':','\'','"',
+         ',','<','.','>','/','?']
+    return ch in isp
+class Input:
+    io_line_buf=""
+    io_line_buf_size=0
+    io_line_buf_cnt=0
+    file=stdin
+    eof=False
+    
+    def __init__(self,f=stdin):
+        self.io_line_buf=""
+        self.io_line_buf_size=0
+        self.io_line_buf_cnt=0
+        self.file=f
+        self.eof=False
+
+    def freopen(self,name):
+        self.io_line_buf=""
+        self.io_line_buf_size=0
+        self.io_line_buf_cnt=0
+        self.file=open(name)
+        self.eof=False
+    
+    def alloc(self):
+        if self.io_line_buf_cnt>=self.io_line_buf_size:
+            self.io_line_buf=self.file.readline()
+            self.io_line_buf_size=len(self.io_line_buf)
+            self.io_line_buf_cnt=0
+            if self.io_line_buf_size == 0 :
+                self.eof=True
+    
+    def getchar(self):
+        self.alloc()
+        if self.eof:
+            return '\0'
+        self.io_line_buf_cnt=self.io_line_buf_cnt+1
+        return self.io_line_buf[self.io_line_buf_cnt-1]
+    
+    def getline(self):
+        self.alloc()
+        if self.eof:
+            return ''
+        if self.io_line_buf[-1:]=='\n':
+            res=self.io_line_buf[self.io_line_buf_cnt:-1]
+        else:
+            res=self.io_line_buf[self.io_line_buf_cnt:]
+        self.io_line_buf_cnt=len(self.io_line_buf)
+        return res
+    
+    def read_int(self):
+        vali=['-','0','1','2','3','4','5','6','7','8','9']
+        S=""
+        ch=""
+        while not self.eof:
+            ch=self.getchar()
+            if ch in vali :
+                break
+        S=ch
+        while not self.eof:
+            ch=self.getchar()
+            if not ( ch in vali ) :
+                break
+            S=S+ch
+        return int(S)
+    
+    def read_float(self):
+        vali=['.','-','0','1','2','3','4','5','6','7','8','9']
+        S=""
+        ch=""
+        while not self.eof:
+            ch=self.getchar()
+            if ch in vali :
+                break
+        S=ch
+        while not self.eof:
+            ch=self.getchar()
+            if not ( ch in vali ) :
+                break
+            S=S+ch
+        return int(S)
+    
+    def read_str(self):
+        S=""
+        ch=""
+        while not self.eof:
+            ch=self.getchar()
+            if isprint(ch):
+                break;
+        S=ch
+        while not self.eof:
+            ch=self.getchar()
+            if not isprint(ch):
+                break;
+            S=S+ch
+        return S
+    
+    def read_char(self):
+        ch=""
+        while not self.eof:
+            ch=self.getchar()
+            if isprint(ch):
+                break
+        return ch
+    
+    def scanf(self,flist):
+        out=[]
+        for tp in flist:
+            if tp == 'D' or tp == 'd' :
+                out.append(self.read_int())
+            elif tp == 'F' or tp == 'f' :
+                out.append(self.read_float())
+            elif tp == 'C' or tp == 'c' :
+                out.append(self.read_char())
+            else:
+                out.append(self.read_str())
+        if len(out) == 1:
+            return out[0]
+        else:
+            return out
+
+IO_inf=Input()
+def scanf(flist):
+    return IO_inf.scanf(flist)
+def getchar():
+    return IO_inf.getchar()
+def getline():
+    return IO_inf.getline()
+
+# math
+def gcd(a,b):
+    if b==0 :
+        return a
+    return gcd(b,a%b)
+
+def lcm(a,b):
+    return int(a/gcd(a,b)*b)
+
+def yf(a,b):
+	c=gcd(a,b)
+	a=a/c
+	b=b/c
+	return [a,b]
+
+#自适应辛普森积分
+'''c++版
+#include<cstdio>
+#include<cmath>
+double a;
+inline double f(double x) { return pow(x,a/x-x); }
+inline double simpson(double a,double b) { return (f(a)+4*f((a+b)/2)+f(b))*(b-a)/6; }
+double asr(double a,double b,double eps,double A)
+{
+    double c=(a+b)/2;
+    double L=simpson(a,c),R=simpson(c,b);
+    if(fabs(L+R-A)<=15*eps) return L+R+(L+R-A)/15;
+    return asr(a,c,eps/2,L)+asr(c,b,eps/2,R);
+}
+double asr(double a,double b,double eps) { return asr(a,b,eps,simpson(a,b)); }
+int main()
+{
+#ifdef local
+    freopen("pro.in","r",stdin);
+#endif
+    scanf("%lf",&a);
+    const double eps=1e-8;
+    if(a<0) printf("orz\n");
+    else printf("%.5lf\n",asr(eps,20,eps));
+    return 0;
+}
+'''
+def simpson(f,a,b):
+	return (f(a)+4*f((a+b)/2.0)+f(b))*(b-a)/6.0
+
+def asr(f,a,b,eps,A):
+	c=(a+b)/2.0
+	L=simpson(f,a,c)
+	R=simpson(f,c,b)
+	if abs(L+R-A)<=15*eps:
+		return L+R+(L+R-A)/15.0
+	return asr(f,a,c,eps/2.0,L)+asr(f,c,b,eps/2.0,R)
+
+def sps(f,a,b,eps):
+	return asr(f,a,b,eps,simpson(f,a,b))
+
+# Data Struct
+def Array(*idx,dft=0):
+    ary=[]
+    idx=list(idx)
+    idx.reverse()
+    for i in range(0,idx[0]):
+        ary.append(dft)
+    for rg in idx[1:]:
+        x=[]
+        for j in range(0,rg):
+            x.append(ary[:])
+        ary=x
+    return ary