p03828 AtCoder Beginner Contest 052 - Factors of Factorial_28759
You are given an integer N. Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

* 1≤N≤10^3

Input

The input is given from Standard Input in the following format:


N


Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
import collections
N=input()

a=[]
def soinsu_bunkai(x):
	if x==1:
		a.append(1)
		return a
	n=x
	flag=0
	while flag!=1:
		for i in range(2,x+1):
			if n%i==0:
				n=n/i
				if n==1:
					flag=1
				#print i
				a.append(i)
				break
	return a


for i in range(2,N+1):
	soinsu_bunkai(i)

#print a

b=collections.Counter(a)
#print b

ans=1
for i in b.values():
	ans*=(i+1)

print ans%(10**9+7)
6 3 1000 8 0 15 18 2 4 9 5 10 7 11 13 17 23 21 42 35 38 54 34 65 30 12 22 20 26 37 19 16 14 25 36 29 27 28 66 43 55 68 31 90 83 44 50 39 24 33 32 41 49 52 56 67 108 111 101 100 110 48 1001 46 45 53 64 59 70 76 40 115 47 102 87 51 116 57 82 63 80 104 107 185 72 75 74 61 60 69 81 62 78 136 97 58 93 71 112 132 109 144 149
30 4 972926972 96
 1
 4032
 14688
 2
 8
 160
 16
 270
 60
 540
 1584
 10752
 192000
 60800
 258048000
 16422912
 60466176
 559756674
 12165120
 105219839
 2332800
 792
 96000
 41040
 532224
 39191040
 29376
 5376
 2592
 340032
 19595520
 1834560
 677376
 917280
 195900610
 516096000
 984916319
 889436190
 4665600
 729407917
 999147209
 677376000
 464046052
 85100544
 242880
 7864320
 5529600
 204871680
 698576619
 87039944
 217548604
 391801220
 875619122
 130571620
 167902493
 583951250
 277966376
 876670706
 513172208
 258709753
 819624960
 174079888
 50952999
 218175167
 845412639
 665186745
 102435840
 813661707
 517419506
 687346296
 775916997
 210846678
 582700142
 16857327
 999573608
 139926156
 790600338
 229757313
 781592107
 591770736
 891132264
 31280490
 316684054
 212862082
 106431041
 472974756
 524719291
 535421074
 764748573
 626955546
 976972733
 609087587
 520705814
 690825271
 574892396
 489345615
 751238237
 464103226
 978268519
