Buggy python submission (verdict: Runtime Error):
import numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import copy as cp
import sysimport numpy as np
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import collections as col
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import copy as cp
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import copy as cp
import sysimport numpy as np
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import copy as cp
import sysimport numpy as np
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import copy as cp
import sysimport numpy as np
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import cmath as cma
import copy as cp
import sysimport numpy as np
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import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
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import collections as col
import functools as func
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import copy as cp
import sysimport numpy as np
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import copy as cp
import sysimport numpy as np
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import copy as cp
import sysimport numpy as np
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import copy as cp
import sysimport numpy as np
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import collections as col
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import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
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import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
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import collections as col
import functools as func
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import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
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import functools as func
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import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
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import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
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import copy as cp
import sysimport numpy as np
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import collections as col
import functools as func
import itertools as ite
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import copy as cp
import sysimport numpy as np
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import copy as cp
import sysimport numpy as np
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import collections as col
import functools as func
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import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sysimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
import numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.inf

k,n = imap()
a = iarr()
dist = []
for i in range(n):
    tmp = a[i] - a[i-1]
    if tmp<0: tmp += k
    dist.append(tmp)
ans = k - max(dist)
print(ans)


Fixed submission:
import numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.inf

k,n = imap()
a = iarr()
dist = []
for i in range(n):
    tmp = a[i] - a[i-1]
    if tmp<0: tmp += k
    dist.append(tmp)
ans = k - max(dist)
print(ans)

Buggy python submission (verdict: Runtime Error):
import numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.inf

import numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.infimport numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.inf






k,n = imap()
a = iarr()
dist = []
for i in range(n):
    tmp = a[i] - a[i-1]
    if tmp<0: tmp += k
    dist.append(tmp)
ans = k - max(dist)
print(ans)


Fixed submission:
import numpy as np
import scipy.sparse as sps
import scipy.misc as spm
import collections as col
import functools as func
import itertools as ite
import fractions as frac
import math as ma
import cmath as cma
import copy as cp
import sys
def sinput(): return sys.stdin.readline()
def iinput(): return int(sinput())
def imap(): return map(int, sinput().split())
def fmap(): return map(float, sinput().split())
def iarr(n=0):
    if n: return [0 for _ in range(n)]
    else: return list(imap())
def farr(): return list(fmap())
def sarr(n=0):
    if n: return ["" for _ in range(n)]
    else: return sinput().split()
def barr(n): return [False for _ in range(n)]
sys.setrecursionlimit(10**7)
MOD = 10**9 + 7; EPS = sys.float_info.epsilon
PI = np.pi; EXP = np.e; INF = np.inf

k,n = imap()
a = iarr()
dist = []
for i in range(n):
    tmp = a[i] - a[i-1]
    if tmp<0: tmp += k
    dist.append(tmp)
ans = k - max(dist)
print(ans)